Possible runner's knee...?

Hi all, I've only recently started running and I've already been sidelined due to pain! I thought I was taking things slowly enough but I guess I wasn't...

A little background...I've been very sedentary for about the past decade (I'm 38). Never had any knee injuries but since I had my daughter 3 years ago I've had a little trouble off and on with some minor right knee pain when going down stairs mostly...a sharp pain with a feeling here and there like my knee was about to give way. When I started running recently the pain was not present. I was fitted for shoes and insoles (Mizuno Inspires) from a local running store back in 2011 when I was 20 pounds heavier but the shoes are mint since I never got round to running until now. I'm now 140 pounds at 5 foot 9 so not overweight, just extremely out of shape. I naturally have a shorter stride and land on my midfoot under my center of gravity with my knees slightly bent. I started by going out for 20 minutes one evening, warming up for a couple minutes with brisk walking, then running for one minute only and then walking until I caught my breath, repeating for the 20 minutes then cooling down by walking for the last couple minutes. I rested the next day and did some squats, lunges and planks. The next morning I ran again for another 20 minutes, doing the same intervals as the first run. I did not rest the next day, but went for another run the next evening (34 hours later) but did 30 minutes that time. My legs were somewhat sore that night but not horrible, and by the next day I was fine. I rested for the next two days...then on my next run the moment I started actually running I had severe pain in both of my knees. I was shocked because up until that moment I was feeling fine. It was so bad I could only run for about 30 seconds at a time, for 2 minutes total. I walked the rest of the way home. By the time I got home the pain was gone, but then both knees started hurting by that evening. Now it's been three days since then and my knees, especially my left, are STILL hurting! Its mostly right under my kneecaps but toward the inner part of my knees. Sometimes it's dull and throbbing, other times it's sharp. I have a hard time walking at times and stairs are killing me. They are tender to the touch and the left one feels a bit warm too. Sometimes the area on the left one feels extremely itchy and almost burns, this started yesterday. I've been icing them and taking ibuprofen, and trying not to walk crazy amounts. Is this runners knee? I thought runners knee only hurt when actually running or going on stairs, etc., but mine hurt most of the time. I'm really down because I was so excited to start running and I can't believe this has happened so quickly. Should I go see a doctor? What can I do to help this go away and stay away once I start running again? I don't see how I can take it much slower...I was already hardly running lol...

Sorry for the novel. I'm just looking for some answers/hope...