At this time and for the foreseeable future having LASIK will DQ you from even enlisting in the Navy at all. CURRENTLY, only the AF allows it. That does not mean it will not change in the next 6-7 years before you complete college but you cannot take the risk until you know for certain. If it does not change and you do not get correction, you will not commission in the Navy Special Warfare Division either out of NROTC or the USNA because you cannot qualify under current standards. If you go ahead and get the correction and the Navy does not change its requirements you will wind up not being able to get in the Navy at all. And while we are talking about DQs...NO FREAKIN' TATTOOS of any kind, anywhere, at any time...and no idiotic piercings, either. Officers do not do that.
You can get the PRK, then wait about 6 months for your eyes to heal properly.
I'm pretty sure the military will pay for you to have eye surgery. Either through PRK or LASIK. But if your eyes are as bad as you say they are, you won't even make it past the first Meps physical.