Q. Someone that has from very dry skin on his hands and thus suffers greatly, can he put some Vaseline on them on Shabbos?
A. Poskim disagree whether rubbing Vaseline is included in the Biblical prohibition of Memareach or smearing (a tolda or subordinate melacha of Memachek. O.H.314: 11). Some argue that it is not thick or dense enough and the prohibition is only Rabbinical, while others even permit on the onset. (Tzitz Eliezer 7: 30, Beer Moshe 1:36 -2: 59, Piskei Teshuvos 314: 11, Shiurei Tahara p. 217, Shemiras Shabbos K. 40: 2, et al). There may be Halacha differences on just applying or dubbing the cream without smearing it and also doing it with a shinui or in an unusual way.
As far as prohibited refuah on Shabbos, it may be permitted due to the significant pain involved. (Shulchan Aruch O.H. 327: 1 – 328: 22, Mishna Berura ibid. 70). See question 2219 regarding very painful dry lips.
Horav Shlomo Miller’s opinion is that one should avoid using Vaseline and rather obtain a liquid hand lotion, that may provide an even better result.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a