I can't guess at what is causing your knee pain, but I can share my situation. I am on my 2nd bout of runner's knee (patellofemoral pain syndrome) and am currently in physical therapy for it. My situation has been caused most likely by weak hips. My PT plan is weight training to strengthen my hips (I've been working on strengthening my other leg muscles since my first round of runners knee, I guess my hips were just slower to develop).
I'm still running about 20 miles a week, but my PT says no stair climbing exercise. Obviously, I walk up and down stairs...but just not a concentrated exercise effort of stair climbing. He says it puts more strain on my knees vs. running. In fact, shortly before my runners knee symptoms came back this time, I was doing a stair climbing group exercise event once a week. My PT is wondering if this activity was the thing that brought my problem back.
If you can see an orthopedic doctor about your knees I'm sure you'd get some great advice! My PTs have said that women are more prone to knee issues because of our wider hips. Means your thigh bones come to your knee at more of an angle vs. men. And knee problems often stem from an issue further up the body...like hips, quads, glutes, etc.
Best of luck to you!