As someone who's been a competitive swimmer for many years, my input is this:
You state that you're doing 3x martial arts and 1x gym workouts per week, which can be plenty or not enough depending on your physical fitness level. It's up to you how much swimming you want to incorporate into your busy schedule, but one way to approach your situation (to avoid further knee problems for now, at least) is to make swimming a bigger priority than the other two. This means swimming 3-4 times/week, starting each following day with a warm-up of 100 extra yards and working down a ladder at a slow to medium pace, before getting to the high intensity part of the workout.
For example... if you swim on Monday, Tuesday, Thursday, Friday... slow to medium pace warm-up would be like:
- 1st Monday: 100 yds
- 1st Tuesday: 200 yds then 100 yds
- 1st Thursday: 300 yds then 200 yds then 100 yds
- 1st Friday: 400 yds then 200 yds then 100 yds
- 2nd Monday (cut back 100): 300 yds then 200 yds then 100 yds
- 2nd Tuesday: 400 yds then 200 yds then 100 yds
- 2nd Thursday: 500 yds then 200 yds then 100 yds
- 2nd Friday: 600 yds then 200 yds then 100 yds
- 3rd Monday (cut back 100): 500 yds then 200 yds then 100 yds
- and so on...
Always use freestyle (the crawl) for the first rep in the warmup set, and after that you can mix strokes for the remaining reps of the warmup set if you want. I find this works extremely well for me. After the warm up set, on days when I'm up for it I will throw in plenty of short burst, short distance HIIT (high intensity interval training) reps using my favorite strokes. You can do the same. By doing this, it's possible to get cardio to a comfortable zone all around and eventually swim miles nonstop.
Just remember that muscle recovery and eating well is just as important, and you'll do great with cardio.