I had a baby about 3 months ago and ever since I have been noticing stiffness and pain in my joints, when I get up from sitting, when I climb stairs, even when I'm lying in bed. There's mostly stiffness and pain in my feet, knees, and my legs. I keep walking every night hoping that will make me feel better, but it keeps getting worse. Is this normal after just having a baby, or is this something I should really be concerned about?

I don't think that is normal, and I don't think it is related to the birth of your baby. It could be many things and without consulting your doctor it would just be a guessing game. Have you been running a fever? How is your appetite? Try to think of all the things you can that don't seem quite right, including the pain & stiffness, and make a list to bring with when you see your family doctor. Does Arthritis, or Lupus run in your family? I don't think you should be scared, but I do think you should be checked over by your doctor.

If you are concerned enough to post the question here, then you should go see your doctor.
Having a baby can be very tough on your body and you're carrying your weight in a completely different manner now. You're also lugging around a baby and adjusting to an entirely new lifestyle. The cramps and stiffness may be related to that. You may want to take warm baths with soothing bath salts, try a heating pad, that kind of thing. Also, make sure you are getting plenty of calcium. But do NOT take ANY sort of pill or drug without consulting your doctor.
I think that you should check with your doctor anyway. At least give a call and describe your symptoms and see what s/he thinks. There is no way that anyone can 100% diagnose you, on line.