There is no argument that will convince her, don't even try. She believes in allopatic medicine and allopatic medicine is a religion. It's based on the "fact" that doctors know everything, it is the starting point. When you tell her that it is not so, it's like telling a Christian that there is no God. Therefore her anger - put yourself in her shoes, we all defend what we believe.
"If it worked it would be FDA approved", or "If it was good my doctor would know about it" or something like that, I heard it many times already
By the way, it's good that you had second thoughts and re-checked the facts. Shows that you are not religious.