Definitely ask your doctor what exercises they'd recommend first. Because they know you better then we do, they are in a better position to make suggestions.
Now, one thing you could do is ask them about chair aerobics. If you find it difficult to stand for long periods of time because of the swelling in your legs, sit in a chair and do upper body exercises. You could use hand weights or resistance bands to do upper body strength exercises. Coach Nicole does have a 10-15 minute chair workout posted in the fitness section. There are also chair workouts posted on YOUTUBE. Watch them and decide which ones you may be able to do.
Ask your doctor about swimming or water aerobics. Being in the water can help take stress off your legs and joints.
One thing you might do, is read this great Daily Spark Blog by member INDYGIRL. At one time, she weighed over 460+ pounds. She too had limited mobility, but was still able to get in some regular exercise. This may give you some ideas. But once again, check with your doctor to make sure it's okay. www.dailyspark.com/blog.asp?post=4_workout