Is it normal to have swelling and numbness after having carpal tunnel surgery a month ago?

possibly: Numbness of what in particular? Is this the numbness you were having prior to the surgery or new numbness? And swelling in the hand around the surgery? Well i tell my patients that are having carpal tunnel release surgery that resolution of the numbness is variable, depends on how long the symptoms and how severe the nerve injury. I dont promise resolution of numbess/tingling.

Yes: Hand swelling is common after a carpal tunnel release. Take it easy on the hand for a few weeks and the swelling should resolve. I tell my patients to give the hand a chance to heal.