I've had issues with my knees since I tore them all up at 14 years old.
If it is an injury, you need to be super careful not to make it worse. When I push myself too hard, I'll have some stiffness and pain in the joint, and the soft area directly below the kneecap becomes inflamed and feels weird to the touch. Over time, with regular exercise without overdoing it, the symptoms eventually relax to where you can push a lot further without it bothering you.
Muscles can also just remain sore for several days, and if you aren't swelling or experiencing severe pain, it may be possible that it's just muscle soreness. If it bothers you pretty bad, take a little time off running and try something with less impact on your knees, like walking.
Also pay attention to the surfaces you run on - certain treadmills mess my knees up after about 5 minutes of running, pavement kills me after about 30. Dirt or an actual running track I can run on indefinitely without any pain or problems. You might see if changing the surface you run on has any effect on it.