"itis" means inflammation, and inflammation can have many causes. It could indeed be the diarrhea. If that's the case, an antibiotic (unless his bowel problems are a result of a bacterial infection) is likely unnecessary and can cause a microbial imbalance that can make him more suseptible to things like candida (yeast).
Has anyone retracted his foreskin? IMO, it's really too early to be doing that. Trying to pull it back while he's so young may very well cause further irritation & microtears in the tip, which is painful and creates an entry point for bacteria and can lead to infection/scarring. Is the cream a prescription? It's not something like Neosporin, is it?
I'm not sure I'd give my son systemic (internal) antibiotics unless he was extremely ill and we didn't have time to get a culture before starting an intervention. Otherwise, I think I'd want a culture/blood work done before I'd consent to antibiotics. I think they're used way, way to casually these days.
Maybe give him some probiotics (like, acidophilus supplements); that should help get his bowels healthy again, too.