Your County Public Health Office should be able to do all necessary vaccines. My understanding is, if you've already had the HBV series as a child, get the titer. If the titer is positive for antibodies, you're set, and you provide documentation of receiving the series and the titer results. If the first titer is negative, you do the full series and second titer. Or, you could just go for the whole series + titer regardless.
If you can, I highly recommend doing the TB skin test over the IGRA. It's cheaper. However, a lot of people (like me, yay delayed hypersensitivity) are allergic to the skin test and have to get the IGRA. Your county public health office should also be able to do this.
Other places to consider, since public health usually doesn't take insurance: other doctor's offices, local hospital, your school's student health center. A lot of times, you can ask your doctor to order the vaccines/skin tests/blood tests and you take the order to your local hospital/whatever hospital your FP is associated with.
If your insurance doesn't normally cover stuff like that, tell them it's medically necessary because you're a medical student and they may or may not pay for it.