What kind of license would you need to have to be able to administer prp shots?

Since the plasma injections come from the patient's own blood, someone who is a medical doctor (M.D.) is able to administer PRP injections.

This is very dependent upon the jurisdiction such as the state you're in. Generally; MD, NP, PA, RN can all perform the procedure. Whether or not you are in a state that permits certificated individuals to perform the procedure, I'd still stay with the licensed practitioner. They are better trained to handle medical problems should they arise.
Hope the above helps.
Warmly,
Arbella Sarkis, MD