Is it possible to overdo it with pelvic tilts and bridges and damage anything in my pelvis? need to strengthen core?

If you truly overdo any specific exercise, muscle, joint pain and pelvic discomfort will be the first symptoms to appear as your body's warning. You can't damage anything if you listen to that warning. When you have discomfort, you should back down, let that part rest for a couple days then resume with a reduced time or force. If pain recurs in a shorter time you should quit that movement.