Is it possible to transfer branches (Army to Navy) and change my MOS (25C to Navy Corpsman)?

https://www.navy.com/locator.html?cid=ppc_gg_b_stan_core&mkwid=sRLj2haLP|pcrid|{creative}|pkw|navy%20recruiter|pmt|e|pdv|c|

SGT (Join to see) Below is some information about Interservice transfers. Since your ETS is near, have you talked to a Navy Recruiter about signing up to become a Navy Corpsman, after your current enlistment is up? Good luck!

https://www.thebalance.com/transferring-between-military-branches-3357016

SFC Fullerton nailed it on the head. In all honesty the likelihood of transferring from Army to Navy is very very slim. Best bet would be to transfer within the Army if possible. You're actually in a better position than most, being that you're a 25 series. The longer you stick with it the more opportunities will become available. Although, if your mind is made up start with a Navy recruiter and than your Army retention NCO. DON'T get out without a plan or education. Best of luck!

The Navy would have to be accepting Prior Service applicants for enlistment. Each branch has their own policies regarding prior service enlistments, which fluctuates based on the current needs of the service. The other issue would be, if the Navy is currently accepting prior service applicants, what MOS are available? For the Army, prior service applicants are limited to a short list of "needs the Army" jobs for your pay grade, and if you are already MOS qualified in one of those, that may be your only option. You will need to contact a Navy recruiter to find out their current policy on prior service.

Is there a specific reason you want to go Navy, as opposed to staying in the Army and becoming a 68W? Not sure about the Navy, but I know that all Army Medics are National Certified EMT-Basic. Maintaining that certification is a requirement for staying a Medic. An added bonus that will give you a leg up should you ever decide to make a civilian career out of it.