Can amoxicillin actually affect birth control pills or is that just in theory? has there been any research or studies that prove this?

Not aware of one: There are many drug interaction websites. There are many different BCPs available. You don't mention what BCP. You can easily check if anything mentioned. In general I would be very surprised if there was one because of the class of the drugs used. Doctors don't have infinite memories but the Web does if it has ever been recorded there.

Now felt to be false: The current thinking is that except for rifampin, other commonly-used antibiotics do not alter the effectiveness of birth control pills. This is likely presuming a person is not sick with vomiting or diarrhea, or some other condition that decreases the absorption of a swallowed pill. One can look up: http://www.ncbi.nlm.nih.gov/pubmed/12063491