Wanting to change schools because your current school doesn’t have your major is a valid reason to transfer.
Are you certain you want to transfer, or will you transfer only if it’s T20? If the former, you will need to apply to some match schools, and an affordable safety to make sure you will have the option to transfer.
I can’t chance you, but transferring to a T20 will be a reach for all schools…being URM will help you though. How strong will your LoR(s) be from your college prof(s)? Are there any Cs or Ws on your transcript?
Good luck.