61.195 Flight instructor limitations and qualifications
(d) Limitations on endorsements. A flight instructor may not endorse a:
(1) Student pilot's logbook for solo flight privileges, unless that flight instructor has -
(i)Given that student the flight training required for solo flight privileges required by this port; and
(ii) Determined the student is ...
14 CFR Part 61.39 (a)(5) states that you can not take a checkride in the US until you are of age to hold the desired certificate.
(5) Meet the prescribed age requirement of this part for the issuance of the certificate or rating sought;
Sorry. I encourage you to take as many mock-checkrides as possible in the meantime.
Also, in addition to mock-checkrides. ...
Necro-ing this question to give a more forceful opinion of "OP was not wrong."
First, like GreenAsJade said, tower didn't yell at you in the moment. This is not incontrovertible evidence of legality or correctness, but it's a pretty strong piece of evidence.
More importantly, "report three miles out" is not a standard pattern entry. Here ...