I have the same problem, they are so painful , the pain and damage is caused by the stairs, avoid them if you can as much as possible.
when you are climbing the stairs the pressure on the knees is 7 times and when coming back 11 times of your weight, it causes a big damage.
It could be a variety of things, but I'm guessing it has something to do with damage caused during your dancing years that went untreated.
If you don't feel safe carrying your baby, get to a doctor and ask for a referral to an orthopedic surgeon who specializes in knees. Maybe you can get by without surgery, but a knee specialist will know what to look for.