I'd call up the PRIMS help desk to get started, ask them if they can still look you up by your old DoD number.
Tactically and tactfully, after you talk to the person on the phone and get their contact info (other than
prims@navy.mil or whatever it is), if I were you I might email them from your personal email and start with a "thank you for helping me earlier today in our phone conversation..." thing, with your officer recruiter's email cc:'ed. I
think your PRT results might be protected by the Privacy Act, but getting them into your OCS package is appropriate use of them. The obstacle is that the PRIMS people and your recruiter both have to work within the bounds of that, but once you've directly connected them then one can email the other using officially NMCI encrypted email and then nobody has to worry about getting in trouble for an information spill.
Silly and bureaucratic as that sounds, of course don't tell your recruiter you think it's silly.
Part of the gamesmanship of applying to OCS is doing the legwork yourself, and this is certainly legwork. Yes, you'd think it would be easier for your recruiter to just call up PRIMS directly, or that the NRD ought to already have a system for prior enlisted but now separated applicants just like you (you're not the first, far from it...).
Anyway, just grin and bear it. The commission is worth the price of admission.