I was diagnosed with a type of Runner's Knee many years ago - Iliotibial Band Syndrome. Your description sounds like what I was experiencing. According to the
Runner's Blueprint web site, Runners Knee occurs when cartilage in the kneecap becomes irritated. It can have many causes.
According to the running doctor who I saw, my knee pain was primarily caused by running too much on heavily crowned roads, exacerbated by poorly-cushioned running shoes and a minor leg length discrepancy. That was causing my Iliotibial Band to rub against the kneecap, causing pain mainly at the bottom of the kneecap. YMMV.
The doc said that most people have some sort of leg length discrepancy. In my case, that was mitigated by putting an extra heel pad in the shoe that went on the shorter leg. The doc told me to stop running for a short while, and get some real running shoes. He made makeshift orthotics/arch supports for me to use and gave me some stretches (like
these) to do to stretch my Iliotibial Band prior to and right after running. That worked for me, and I was able to do some significant distances after that, including a marathon.
If you have good health insurance, it probably wouldn't hurt to see your local running doctor. Insurance might even cover some orthotics.