Im taking penicillin for strep, since taking them i have really sore breasts, can penicillin make my breasts sore?

Doubtful: Anything can happen. But sore breast due to penicillin would be a new side-effect. Would suspect another cause. Are you pregnant? Have you started new birth control medication? If this persists, see a doctor.

Not necessarily: Not necessarily, provided the soreness is not associated with a rash or some other skin eruption on your breast which might be a reaction to penicillin. Penicillin medications, like many other drugs, can cause allergic reactions. If the soreness was related to the penicillin i would assume the soreness would go away once you completed your treatment with penicillin.