Losing weight

I injured my knee back in October because I of an incident that occurred and last month I injured my back and caused me to sprain my muscles of my back. Is it possible I could workout (swim) since I am limited to only that since I can't workout lower or upper body. I use to be able to do that before my incidents which sucks now but I need to lose weight and I was wondering if I could swim and be on a strict healthy diet so I can lose more than 20 lbs in four months before the summer....