I've found NSAIDs to be contraindicated except for the special case of tendonitis, and even then they should not be used unless necessary.

Knee problems, like back problems, respond best to careful exercise and training. Exercise may need to be targeted to resolve the problem. That said, Friel reviews several studies on compression wear here:
Joe Friel - An Update on Compression Clothing

A feeling of soreness inside the knee may be due to cartilage/meniscus damage. Frequently there's nothing to be done about that other than to train to ride in lower gears, i.e. spin faster, in the 100 rpm range even when climbing. I've ridden with older runners who are missing much of the cartilage in their knees. They spin fast and take ibuprofen. Nothing to be done, it just hurts. That said, I've had less knee pain since I've been taking glucosamine sulfate and MSM, starting about 10 years ago. I've found hiking hills to be the best cross training for cycling.