PRK, LASIK, and corrective lenses (contacts or eye glasses) are all permissible and widely used by the Navy.
When I was in college in 2005, I failed the eye exam at MEPS (after a PROREC for OCS). I paid to have PRK done at a civilian doctor, which delayed getting my final select by 3-4 months (3-6 months is not uncommon depending on how bad your vision was to begin with and what procedure you have done—disclaimer: the length of time may have changed since 2005). While I was at OCS in 2007, they said my vision had degraded and that I needed corrective lenses. After that I wore contacts for most of career while flying F/A-18s until 2016 when I had LASIK done at the Naval Refractive Surgery center in San Diego. I was med down for about 1 month and flew again right away after that period.
The point of my story is that you can have little setbacks in vision and there are plenty of easy-enough solutions. Don’t take no for an answer, and find your own solutions or find someone who knows that they’re actually talking about. No one else cares about your vision of your career more than you do.