I am debating wether to give my 63 year old mother amoxicillin or ampicillin. she is in bed now, and does not have empty stomach. she has slight fever?

No difference: Ampicillin and amoxicillin are virtually identical; either drug is equally effective, but amp is taken more frequenlty and diarrhea is a more common side effect. However, nobody should take antibiotics without professional advice. If she has a bacterial infection, amp or amox isn't necessarily a good choice; best antibiotic depends on the specific illness and the particular bacteria causing it.