DW Runners

I'd love to get some advice, since I am very much a running newbie.

I've always enjoyed running but I'm finally in a place post-baby where I might be able to do it consistently. I went running two times this week (treadmill at the gym). I'm running between 30 min and an hour, in 10-minute intervals with walking in between. What I found was that while both times the running was fine, afterwards my knees ached, enough that going down stairs I had to slow my pace quite a bit. Kneeling is when I can feel it the most. My knees also felt a bit warm to the touch, suggesting some inflammation. And then, I think because I was positioned wrong, I got this...cramp? It felt like my knee went out of alignment somehow, and was quite painful for a bit before it just faded away.

I was wondering if this is normal and I can do something about it, or if it's more that the impact on my knees is too much and I'm doing damage. Here's what I'm thinking:

1. I am getting older and more broken; running isn't the sport for me.

2. I am doing something wrong (either during the run or not enough pre- or post-care, like stretching).

3. This is because I'm just starting and my body will adjust eventually as long as I take it easy and ramp up slowly.

Any idea which it might be (or a combination)? Are there other exercises I can do to strengthen my knees/joints specifically? Is this something to see a doctor/physio about?

Thanks very much!