May one remove a splinter on Shabbos?
It is permitted to remove a splinter on Shabbos [with one’s hands, tweezer, or needle as will be explained]. However, one needs to beware upon removing the splinter to do it in a way that it will not inevitably cause blood to come out in the process of removing it. [Thus,] for example, if the thorn turned upside down while trying to remove it and it is [now] impossible to take it out without extracting blood, then it is forbidden to remove it. [Likewise, if the splinter is very deep in the skin and will cause blood to be extracted upon its removal, then it may not be removed. This follows the ruling of Admur. However, many other Poskim rule that when there is no alternative, it is permitted to remove the splinter even if it will inevitably cause bleeding. Practically, those who follow the rulings of Admur should only be lenient if there is worry of infection and the like, and not due to mere pain, even if it is very painful.]
Using a needle: A whole and working non-damaged needle is permitted to be used on Shabbos for the sake of removing a splinter. [However, if one has a non-Muktzah needle available, such as the needle of a safety pin, then it is preferable to use it over a sewing needle.]
It is permitted to remove a splinter on Shabbos so long as it will not inevitably cause it to bleed in the process. If its removal will inevitably cause bleeding, then it may not be removed unless it will be prone to infection due to it.
May one ask a gentile to remove a splinter that will cause inevitable bleeding when removed?
Yes, if he is in a lot of pain.
May one pluck away pieces of skin with the needle in the process of removing the splinter?
One may puncture and cut through external pieces of skin for the sake of reaching the splinter so longa s blood will not inevitably be released as a result. However, one may not cut off pieces of skin due to the Gozez/Shearing prohibition.
 Admur 308:38; Michaber 308:11; Rambam Shabbos 25:8; Mishneh Shabbos 122b; M”A 328:32; Vetzaruch Iyun why this law was not mentioned by Admur in 328 which deals with the laws of medical treatments!
 Admur ibid; Michaber ibid; Mishneh ibid; M”A ibid
 Admur ibid; M”A 328:32 based on Tosafus Sanhedrin 85a; M”B 328:88 in name of Magen Avraham; Kaf Hachaim 308:96
The reason it is forbidden if the removal of blood is inevitable: As doing so [in a way that will for certain extract blood, transgresses the Melacha of] Chovel [which according to Admur is a Tolda of the Av Melacha of killing, as explained in Admur 316:14, however, according to the Rambam 8:7 it is a Tolda of Mifareik, see also Admur 328:54 who implies that it contains both Chovel and Mifareik] even if one did not intend to extract the blood, as one is removing it out in a way that it is inevitable for blood not to come out [i.e. Pesik Reishei; Lit. “Can you cut off its head and have it not die”] [Admur ibid; Regarding the prohibition of Pesik Reishei, see Admur 337:1; 253:10-11; 28; 259:7; 277:1-5; 278:4; 302:4; 308:38; 314:3; 316:4-5; 21-22; 318:21; 319:29; 320:17; 20, 22-24; 323:11; 324:1; 326:8; 334:24; 336:9 and 17; 337:1; 340:4; 357:3; 646:13] Nonetheless, according to those Poskim who rule that one is exempt for a Melacha Sheiyno Tzericha Legufa [See Admur 316:16], then here too one would be exempt if he transgressed and did so, as it is merely a Rabbinical prohibition of Pesik Reishei Derabanon. Furthermore, even according to those Poskim who rule that Melacha Sheiyno Tzericha Legufo one is liable for, one can argue that here they would all agree that one is Biblically exempt, as it is Mikalkel. [See Sanhedrin 84b; P”M 328 A”A 33; Machatzis Hashekel on M”A ibid; Tehila Ledavid 328:47; M”B 328:88 and Biur Halacha 308:11 “Hakotz”] Nonetheless, this would remain forbidden as we rule that a Pesik Reishei is forbidden even by a Rabbinical prohibition. [Implication of Admur ibid who rules stringently here unlike the other opinions brought below; Admur 337:1; 320:20 regarding walking on snow; 320:24 regarding a cloth on a Barza; 302:20 regarding squeezing; 316:4 regarding closing container on flies; M”A 314:5; 316:9; Taz 315:3; M”B 316:17 regarding bees; However, see the following case in which Admur is lenient by a Rabbinical Pesik Reishei, Vetzaruch Iyun: Admur 314:3, although in that case we have added reasons for leniency, including: a) Ein Boneh Vesoser Bekeilim. B) mikalkel; c) Kilacher Yad. Even there Admur concludes Lechatchila to be stringent.]
The reason it is permitted if the removal of blood is not inevitable: As in such a case the Melacha of extracting blood is being done without intent, and an action that will not inevitably cause a Melacha to happen is permitted even initially to be done on Shabbos so long as one has no intent for the Melacha to occur. [See Admur 320:20; 324:1; 337:1]
 Admur ibid; Implication of Tosafus Sanhedrin 85a that if it will be a Pesik Reishei then it is forbidden; Possible implication of M”A ibid
Other opinions: Some Poskim rule that it is permitted to remove the splinter even if it will inevitably cause blood to be extracted, as this is a case of Pesik Reishei Derabanon [being that removing the blood is Mikalkel, as explained in footnote above based on conclusion of Sanhedrin ibid] which the Sages permitted to be transgressed for the sake of relieving pain. [Sefer Hateruma 254; Tosafus Shabbos 107b; Biur Halacha 308:11 “Hakotz” and Shaar Hatziyin 328:63 in name of Chemed Moshe; Machatzis Hashekel on M”A ibid “The M”A wrote that one is initially to be careful in this as much as possible…although certainly if he is unable to then it is permitted as it’s a mere Rabbinical prohibition in a case of pain”; Tehila Ledavid 328:47; Implication of M”B 328:88 and so he rules in Shaar Hatziyon 328:63; Kaf Hachaim 308:96; Piskeiy Teshuvos 328:51; Possible understanding of M”A ibid that even he agrees to this allowance and simply stated that if possible one should try to extract it without it inevitably extracting blood, although if this is not possible, then he too agrees that it is allowed, as he rules in 328:33 that the Sages were lenient by a Melacha Sheiyno Tzericha Legufa in a time of pain, and so understands in M”A: Machatzis Hashekel ibid; Tehila Ledavid ibid; Biur Halacha 308:11 “Hakotz” and Shaar Hatziyin 328:63] Furthermore, some Poskim rule that a Pesik Reishei is always permitted by a mere Rabbinical prohibition. [Terumos Hadeshen, brought in M”A 314:5; Shaar Hatziyon 316:21; See Beis Yosef brought in Taz 316:3; Admur 314:3 regarding bees]
 Sefer Hateruma 254; Tosafus Shabbos 107b; Biur Halacha 308:11 “Hakotz” and Shaar Hatziyin 328:63 in name of Chemed Moshe; Machatzis Hashekel on M”A ibid “The M”A wrote that one is initially to be careful in this as much as possible…although certainly if he is unable to then it is permitted as it’s a mere Rabbinical prohibition in a case of pain”; Tehila Ledavid 328:47; Implication of M”B 328:88 and so he rules in Shaar Hatziyon 328:63 and Biur Halacha ibid; Kaf Hachaim 308:96; Piskeiy Teshuvos 328:51; Possible understanding of M”A ibid, and so understands in M”A: Machatzis Hashekel ibid; Tehila Ledavid ibid; Biur Halacha 308:11 “Hakotz” and Shaar Hatziyin 328:63; See other opinions in previous footnote!
 Admur ibid; Michaber ibid; Mishneh ibid
 See Admur 308:39 and Michaber ibid
 The reason: Although a needle is considered Muktzah due to being a Keli Shemilachto Lissur, nevertheless it may be moved as is the law regarding a vessel which is designated for a forbidden use, which is permitted to be moved in order to use it. [Admur ibid]
 See the following Poskim who are stringent in such a case: M”B 308:12; SSH”K 20:8; Piskeiy Teshuvos 328 footnote 417; 308:8; See the Following Poskim who are lenient in such a case: Tosefes Shabbos end of introduction to 308; Ketzos Hashulchan 108 footnote 14; Beir Moshe 8:75; Daas Torah 308:3;
 Piskeiy Teshuvos 328 footnote 416; See Admur 328:20 that a Rabbinical prohibition may be done through a gentile to relieve a severe pain, and hence since in conclusion we rule that the inevitable removal of blood is only Rabbinical due to it being Eino Tzericha Legufa and Mikalkel, therefore it falls under the allowance to be done by a gentile in the event that he is in a lot of pain
 See Piskeiy Teshuvos 328:51
 See Michaber 328:28 and Admur 328:32 that one may pop a boil for the sake of releasing pus
 See Biur Halacha 328:28 “Kdei” and Admur 328:37 and 340:3