You also have a right to decline your doctor's recommendations. She can't MAKE you take Depo if you do not want it. That said, she may then decline to prescribe T. But, as stated, she isn't the only doctor out there. If you are uncomfortable (I would have been in your shoes) then decline until you can inform yourself (as you are).
It is not a standard or required thing. It may be her preferred way of doing things, but if you do not want it, you do not have to have it. It is YOUR body.
Jay