One other suggestion to improve your swimming: Get a coach. Shoot, it can be a teenager from your local swim club who can swim laps around you.
Arm stroke technique and getting your speed up is very important. Rock your shoulders as your arm enters the water and get a good glide. Like bike riding, the faster you move, the easier it gets. If you move fast enough through the water, your head tends to plane up, and it's easier to breathe (freestyle).
The ability to swim a mile, run a marathon or whatever is not for the Navy's benefit, it's for you. You will be called on to tap into those reserves of physical endurance in situations and times not of your own choosing. Having confidence in your endurance will help you get through those trials.