throughout this process i have strongly believed that going to top schools would help me out. at first i wasn't getting any interviews b/c of my low mcat, but they are finally rolling in! had i gone to lesser known schools i really doubt i would have gotten 8 interview invitations, many of which were from reputable schools.
that being said, it is definitely possible to get into great med schools no matter where you go. but, i firmly believe that if they have doubt about a candidate's abilities (e.g. low mcat or low gpa), the reputation of the school they went to will factor into things.
if i were you i wouldn't transfer, because you will probably be be fine where you are if you have good numbers and experiences. but i do believe that going to a state school, getting good grades, but not doing well on the mcat will hurt you. so study hard for the mcat!