Focus on the rest and recover first and foremost. It might be a longer lay out of the water than you would like. I assume you have a PT giving you recovery specific to your injury? That will probably give you all the adaptations for LHT.
When you do return to the water, use the water for your low intensity stuff.
While you heal do not do high intensity that taxes your injury. Get on an elliptical or a stationary bike or run or what ever is least injurious. Personally I wouldnt do any high intensity at all until you are through the recovery process to the point that your PT wants you back in the water. If you are burned out take a high intensity break. If you start getting antsy, then you can look at intervals or sprints on alternate cardio forms...something that will give your c-v system the workout but not aggravate your injuries. When your TIME in the water is up to about 60%-80% of normal training volume ...all at low intensity...if you feel no symptoms then you can start to gently work in the more agressive strokes or workouts on a cautionary basis.
Long term you may want to revamp your work with the team, or how many workouts you do with the team and how many you do on your own. I know that can be difficult with a coached team. And then continue the Lifting to help prevent further injury. Maybe you only train with the team twice a week and do your own thing the rest of the week.
How long have you been primal eating? I found that my tendonitis healed rapidly when I started eating PB and I was able to ramp my training back up much faster than expected.
MTA: because it is rare I dont have more to say
"When I got too tired to run anymore I just pretended I wasnt tired and kept running anyway" - my daughter Age 7