Running puts some pretty high impact forces through the knees (roughly 2.5x your bodyweight in impact forces with every stride, if I recall correctly), so getting knee pain and probable inflammation right now isn't exactly unusual. But just because it's common, doesn't mean it's good or normal.
I'd be looking into how you're running, and in what conditions. How stable your knees are in general, and how you perform each stride are both highly relevant factors. A lot of people who haven't maintained exercise from a young age actually unlearn basic movements such as how to walk, run, squat or hinge safely and naturally, and that could be an issue for you.
Here are three common issues people have with running that could cause some harm:
1) Big heel strike with each stride (enabled by soft shoes; barefoot you wouldn't ever run this way), which causes your toes to slam down immediately after, effectively giving you two doses of impact forces from unstable positions. Ideally, you want your feet to come down fairly smoothly and flatly.
2) Insufficient movement at the hips. How much movement you need at the hips will vary depending on pace, but a lot of people don't know how to use their glutes and hamstrings, meaning that they don't properly extend the hips to move forward, causing all sorts of fun body English that can reek havoc on the hips, knees and ankles.
3) Knees caving during the stride. Largely related to the above 2 issues, but also to lack of strength in the muscles surrounding the knees, people's knees often bend inwards as they run, causing uneven loading. Under 2.5x their bodyweight in impact forces. Over thousands of repetitions.
Beyond that, like Eric I'd highly recommend doing some strength training around the knee, and the exercises he suggested are good ones. I'd agree with starting out light, but I wouldn't necessarily recommend staying there, as progressively building up the load will increase muscle strength and thus stability. I'd also recommend doing step ups or split squats to build active stability; and glute bridges or hip thrusts to practice full extension of the hips and build hip strength and stability.