Do antibiotics affect exercise? I was prescribed amoxicillin for gum infection, but I also have a 10k coming up. Will it affect me at all?

Should not. May want to consider taking a probiotic.
No. Penicillin class of antibiotics such as Amoxicillin should not interfere with you capacity to exercise. Strenuous exercise with certain antibiotics (i.e. Flourquinolones) are relatively contraindicated.