There are a bunch of reasons---here is the first one that I thought of---the VMO which is one of the Quad muscles is often the last to get fit. My own VMO lagged behind for a couple of months before it really started working out with me. That is what controls the inner leg and might have an effect on your inner knee. Second, the stance you are using to climb stairs might be putting more weight on your medial side. And finally, your quad might still be weak and if so, you would feel it in your medial side more than the lateral side.
When we go to PT, we can see our muscles getting stronger, but really, they will not be at their peak until many months have gone by. For instance, last night in pre ski conditioning, I sat down at the lat machine and just pulled it down---as I was pulling, I looked at the weight and it was 60 lbs. I can remember that I used 20 lbs when I first had my surgery and got up to 40 lbs at three months. Now, five years later, i easily pulled 60 lbs---I have not focused on back muscles at all---it is just that I am more active than when my knees were bad and I am stronger overall. Be easy on yourself, recovery takes a while.