My nose is pierced and although I don't put makeup near it, I do use a triangle sponge to smooth into that area. After it heals, you can take it out on a regular basis and clean the stud with alcohol.
You don't want to take it out before it heals which might be a while. I lost mine on accident and it took me 3 days to get back in to have it replaced and ended up having to have it pierced again. Believe me --that 2nd piercing was MUCH worse than the first time.