If you haven't had knee problems before, then it could be a low saddle. A too-low saddle will put strain on the top and inside of the knee. But, alot of the time a low saddle will aggravate both knees fairly equally. So, my outside guess is that you have a pre-condition in your right knee that you probably weren't aware of. The idea is not to have to lift your knees so high because it's like taking two stairs at once with a bike on your back. Many people think that they should be able to dismount from the saddle, so they will lower it to the strain point. Seems instinctive enough, but it's the wrong approach. You dismount from the bike by coming to a stop, them sliding forward to put your foot down at the same moment, or some variation thereof.
Do you know the basic saddle height rule-thing?
Adjust the height until your legs are almost straight at the bottom of the stroke. If your pelvis rocks from side to side, the saddle is too high. If you have to point your toes to reach the pedals, too high. Bring it back down a tad. Even if it turns out that you have a trick knee, it will help.
Another thing, and this is a personal call because you don't ride very far: SPD's (clipless) help a great deal because they allow you to spread the effort around the crank stroke. Thus, you aren't having to concentrate your power at your weakest point.