Yes those are normal side effects from the amoxicillin. Contact your doctor and tell him what is going on it is very likely that he will change your antibiotic to something you can tolerate better. This does not mean you are allergic to it but you can say that you have an intolerance to it.
When I Take Amoxicillin My Guts Go Crazy With Terrible Gas Pains, And Diarrhea. What's Wrong With Me?
Nothing is wrong with you, those are common side effects from amoxicillin. Try some Imodium AD. Best wishes.