Will taking a probiotic together with amoxillcillin antibiotic ease the diarrhea & stomach cramps ?

Probably: Yes. Also try taking the amoxicillin on a full stomach and consume 3-4 small containers of yogurt/day.

Yes: Evidence shows that probiotics ease symptoms of antibiotic associated diarrhea. Caution though: are the symptoms really antibiotic associated, and what is the quality of the probiotic? Because probiotics are considered a food rather than a drug and are therefore not regulated by the FDA, you have to check that what's on the label is really in the bottle. Hope that helps