Doctors don't know everything and they certainly don't know how a drug will affect you. Not all doctors, but a lot appreciate an informed patient. It is YOUR health care and YOUR life. As stated above, you know your body better than a doctor, and a good doctor will listen to you.
I have also tried a lot of different meds and after YEARS of trying different combinations finally have the right meds for me.
There is not a thing wrong with doing your own investigation on what's available these days. In fact it's easy to do with the Internet.
A smart patient participates in their care. Not just be a lump that has no input.
"Shopping" is maybe not the best word for it, but reading up on meds and other's experiences with them is a really good way to evaluate if it's a good fit for you.