Yeah, swimming, Eliptical trainer sounds good, REST and take qualified Medical advice.
So you can ignore my post, it's just my experience.
Minor point, I was playing football in an indoor Gym. 4 a side. It has a Brick floor with a light vinyl covering. My knees were so sore, even though I was teaching Thu & Fri, I had to go forego my own training under Sensei 'cos my knees weren't up to it and I had a marked limp to protect one of 'em. Be careful.
Get really good shoes. Loose weight(I know you are trying to do that anyway.)
I myself have very bad knee and cannot even squat down anymore without great deal of pain, but I do elliptical machine and not only save my knees but maybe my life, as I was in hospital with cardiac problems and doctor said I had to lose weight but hard with bad knees, as you know also. But with elliptical machine I lost 50 pounds and now it is 3 years later and still keep same weight thanks to elliptical machine.
kettlebell swings , snatch and cleans are excellent for cardio
x2 on checking knees with doctor