Whether your counselor can write the letter will depend on what his credentials are -- his degrees and licensing. Generally, a person needs to have a Ph.D. (or equivalent) and a state license to comply with the WPATH requirements. If he doesn't meet them, the chances are fairly good that he's working with, or supervised by, someone who does, so he might be able to refer you (or get that person to sign off on the letter, if it's a supervisor).
There are also clinics and practitioners who operate on an informed consent model, which doesn't require a letter. Given that you're a minor, your parents would probably have to be closely involved if you went that route, but if they're on board with you starting T, that shouldn't be a problem.
Best of luck!