Given your history of shoulder injury, I'd stay out of the weightroom and stick to swimming. If you pool doesn't offer them to the public (the one I work at does), then I would recommend investing in a pair of paddles and a pull buoy. Paddles are about the surface area as your hand, strap onto your palm, and are a very thin plastic. They add resistance to each stroke. Pull-buoy are the white things people put between their legs to keep them floating.
No, your swimming routine is not odd at all. You've actually stumbled upon what top-level athletes do. In order to focus on their arms, they use paddles and a pull-buoy and do exactly what you're doing. You don't
really need the equipment, but it can help, and you won't look as funny
If you're doing freestyle, make sure you do an s-shaped pull underwater, and be sure to flick your wrist out of the water at the end of your stroke. Not only will these make you go faster, which you're probably not too worried about, but they'll improve the workout. Doing the s-pull should help work your biceps a little bit more, to balance out the great workout your triceps are undoubtedly getting.
If you're confused about the pull, or want some more tips, just ask one of the lifeguards. If they know anything about swimming they should be able to show you.