Q. Can I use Afterbite on a mosquito bite on Shabbos? It is not medicine, but it relieves the itching?
Can one anoint oneself with oil on Shabbos, for example rubbing oil on one’s arms?

A. Shulchan Aruch (O,H, 327: 1) rules that one who experiences discomfort on Shabbos may do things that healthy people normally do, even if his intention is to relieve the discomfort. For example, one who has itchy skin may apply oil that healthy people apply as well. One may also apply oil to one’s hands and lips, since nowadays people do so even when their skin is not chapped or cracked – to soften them or for the pleasant feeling. However, you may not apply paste or cream.
Horav Shlomo Miller’s Shlit’a opinion is that using any liquid designated specifically to stop itching, is not permitted, since normally it is not used and is therefore seen as medicine. (See Shulchan Aruch O.H. 328: 44 and Mishna Berura 141, 142, – Shemiras Shab. Keh. 25: 28).
In regards to placing the itch-relieve medicine indirectly, such as outside of the bite and then letting the liquid run down into the affected area, the Rov’s opinion is to be stringent. However, when needed for children it is permitted.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a