I was already 18 by the time I knew I was trans and started hormones, so I don't have any personal experience/anecdotes, but usually HRT is not given to people under the age of 16. Usually. If anything, minors are usually thrown on hormone blockers until they're 16-18, depending on whether they can acquire their parent/guardian's consent.
Also, don't look at the therapist's letters as the be-all, end-all approval for HRT. Think of them as confirmation that you're of sound mind to know that you want HRT and are mentally capable of handling it, but it's a doctor's duty to determine whether you physically qualify. The same goes for top surgery letters—your therapist may determine that you're mentally ready to handle that commitment, but if the surgeons in your area require you to wait until you're a year on HRT to get it, then that's out of the therapist's hands. It's pretty difficult to force a doctor's hand, especially as a minor.
All this being said, keep trying, maybe you'll find someone willing to monitor your health under HRT and grant you a prescription for T.