I got my cavities filled today and I still feel a bit of pain every now and then in addition to feeling different in my teeth. Is it normal?

Yes. Remember, you just had surgery. Expect a few days of altered sensitivity. OTC pain reliever may be helpful. Recovery should be quick.
Common Thing. Some sensitivity is normal after any tooth has been worked on, if there has been multiple tooth decay. As a general rule, if you are still in pain after more than two weeks you should visit your dentist.
Yes, normal. You just had dental surgery. It will take some healing time to feel back to normal again. Assuming you saw a licensed dentist, you should be fine. Teeth will "complain" a little sometimes after a filling is placed.