Exercise IS important, but you shouldn't totally ignore the pain either. Pain, is the body's way of saying that something isn't right. That's not to say we shouldn't exercise when our back hurts though. Give bike riding a chance. Even if it's a stationary bike.
Swimming is also an excellent exercise.
Just make sure you don't spend more time relaxing than lapping. There's bound to be one or two that don't put any stress on your back or knees. As you mentioned earlier adding weight resistance training to an exercise regimen is great too. People that are flat-footed frequently have this problem. You can buy some inserts at a local drug store that will generally help with the pain.