M.R.
My daughter who is 6 had antibiotics (clindamycin) and she got a butt rash that took 6 months to clear up! It was so annoying. I tried everything! Basically, I ended up putting aquafor on it a few times per day and eventually it cleared up. Also, she was complaining of tummy aches for a whole year after (never did she do that before the antibiotics). Basically, the antibiotics clears out a lot of the good bacteria in the gut and it can take a long time to restore the gut. When the gut is out of balance (lack of good bacteria or too much bad bacteria), it can cause skin problems, hence rash on butt. Also, the stool is probably different than it was prior to antibiotics, so that can irritate the butt if there are too much bad bacteria in stool. Of course, I am not a doctor, so this is my personal opinion of what could be going on. It can take a while for the gut to heal after antibiotics. And when the gut is out of balance, other symptoms occur since most of the immune system is in the gut. Hang in there, don't worry too much. My daughter doesn't have a but rash anymore and hardly ever complains of tummy aches anymore. The gut will restore, it just takes time and good eating. I give my daughter lots of yogurt since it helps replenish good bacteria.
I would have the doctor look at it and make sure it's not a yeast rash or a strep rash, or something else. Strep can re-occur, it is very common.