Is it normal to feel this much pain when i got swollen face from infected teeth that are crowned less than a year ag? am on antibiotics and painkiller

Depends: Cannot tell you much without examining you and seeing some images of the areas. However, if there is infection in the gum tissue or the root tip areas or both, then until the cause is corrected, the pain can be great. You should see the specialists in prosthodontics, endodontics, periodontics, and oral surgery, if needed. You might start with the prosthodontist, and they can refer as needed.

Yes it is normal: With a dental infection, there are 2 sources of pain- swelling of the tissues ; destruction of the tissues from bacteria. The antibiotics will kill bacteria ; the pain killer may work on inflammation. It sounds like you may need a root canal to treat the infected tooth. If you had a root canal ; it still hurts, i would recommend that you see an endodontist- a root canal specialist to investigate.