Breastfeeding while on Amoxicillin/ teething rash?

Advice for first time mom please! 2 issues going on that might be tied together… First- Telehealth Dr said I have strep on Fri so I’m in day 3 of Amoxicillin and have 5 more days to take it. I think it might be upsetting his belly. Can I pump and save the milk for when he gets sick since it has antibodies in it or should I dump it??

Second issue- My 4 month baby is breastfed and is teething (doesn’t feel like they’re cutting through yet just constant chewing and drooling for the past 2 weeks). Hes a little more fussy this weekend. He’s been having loose stools and light-mild pink bottom, but today I noticed small white bumps on his bottom and his neck is broke out from the drool (red and bumpy). I’ve been mainly using A&D white Aquaphor on his bottom. Switching back and forth with clear Aquaphor and coconut oil for his neck. Any helpful tips? I’ve got some colostrum I’ll put on him next time I change him and thawing some milk gor a bath to soak in tonight.

Could rash/diarrhea be from teething or the antibiotic I’m on?