I had a very similar problem when I was about 22. My partner and I were going to attempt Black Kaweah via the HST. We camped the first night near Hamilton Lake (about 18 miles from the TH) and I woke up that second day with a nagging pain in my right knee. Like yours, that pain was also centered on the outside of the joint. There was a distinct and painful 'clicking' sensation every time I bent it.
Though painful, it didn't seem too debilitating so we decided to continue on hoping that it could be 'walked off'. That strategy proved to be wrong, however, and I called a halt when we reached Precipice Lake. It was just too painful to continue. We camped there for a couple of days to rest it and then hiked 20 miles all the way back out to the trail head- surely one of the worst days I ever had in the Sierra.
When I got home, I looked up 'Tendinitis' in my brand new copy of Wilkerson's, "Medicine For Mountaineering
" and found it was almost an exact match for my symptoms. Treatment called for warm moist heat therapy and stretching (to prevent chronic stiffening of the joint). I followed this procedure and five weeks later, my partner and I were able to make an attempt on Shasta which involved 7000 feet of climbing- all without any knee pain. In fact, to this day, I've never had that particular problem again.
Years later, we realized that my knee problem may have saved our lives. We were way too inexperienced to be messing with a peak like Black Kaweah.