As for ice, 30 minutes is about all you should need to ice it, and all you would want to ice it. A half hour is enough to help reduce the circulation in the area and minimize swelling, but not so much that you start to see skin changes from the cold contact. If the pain persists, your choices are to take a break from running for a few months and switch over to some non-impact cardio, then try picking up running down the line. If the problem is still there, have it evaluated.
A physical therapist would have you do stretching and strengthening to help give the knee better support and function. If they couldn't help you, an orthopedic surgeon could tell you if there were some underlying structural problems that focus undue stresses on the joint. I get knee pain that comes and goes. With running, it often means my shoes are shot. It started in my 20s, probably from too much basketball on ill-designed joints. Now when I walk up a quiet, carpeted staircase, it sounds like someone is wrinkling a candy wrapper inside my left knee. It's very unnerving. I know that developing the supporting muscles helps, but I'm told I've done myself no favors with all my favorite climbing and squatting drills, so definitely have someone look at yours if it persists. You only have one pair, and it's surprising how much you miss them when they're gone.