You're probably burning more calories than an efficient swimmer just because as an inefficient swimmer, it takes more energy to swim poorly than not. As you get more efficient, you will definitely be able to swim longer. That takes time, as swimming is extremely skill-based.

That said...

Swimming is not the world most efficient exercise if all you're looking for is the calorie burn. The whole Michael Phelps eats 12,000 calories a day thing is about a large young man training 6-8 hours a day to compete in the Olympics. We mere mortals have a different issues to deal with.

In general, swimming does give a good calorie burn, but where it does fall down is the afterburn. You're just not building up the heat you would for dryland exercise, so you're not extending that slight extra calorie burn like you would for running or biking.

However, very few swimmers actually swim yards and yards without stopping. (I'm one, but I am a weirdo with odd goals). Most swimmers train by breaking up their workout into sets -- often no more than 500 yards/meters at a time (so a max of 20 lengths) then resting between those sets. Interval training, as I am sure you are aware, is excellent cardiovascular training and generally gives you a good fat burn, so if that's really the reason you work out, check out some swim workouts that have you swim really hard for a distance, then rest for 10-30 seconds between sets.

Dont' worry about your stopping and starting-- like @NoelFigart1 says, an inefficient swimmer is still burning a heck of a lot of calories.

Depending on the nature of your injury, you might also try some water aerobics/ water PT type moves- (see e.g., http://www.moveforwardpt.com/resources/detail/top-10-exercises-to-do-in-pool)

FYI, although I was a long-time swimmer beforehand, I credit aquatic physical therapy and swimming with my recovery after I had a total ankle replacement in June of 2014.

One thing I do have to be careful about is that almost two years later, I am still prone to foot cramps in the "bad" foot. I do a foot arch/hamstring stretch before and after I work out on the pool ladder: standwith the balls of my feet on the top (dry) step, and lower my heels as far as I can (below the level of the step) and hold for about 20 seconds.

Plantar faciitis is what put me in the pool too. Look for a water fitness class. I found my first class a year and a half ago, and haven't looked back. We do tabata on Mondays (HIIT) and T/Th are the "Long slow burn" days. It's a great cardio workout, if you can get a good instructor. My glasses usually fog up from the effort.

Interval training/ sprints will jump that heart rate right up there!
Distance covered after the session will be shorter, but I imagine it involves some good burns!
May sound obvious too, but the faster you swim and the more you exert yourself, the more you burn!
Many will have a slow leisurely swim and tell themselves they expect high burn numbers!
Ummm....No!