Is it okay for the hand to swell after upper arm surgery?

Maybe. The first thing I would check to see if the dressing is on too tight. Depending on the surgery this too could be the cause. Carring the arm in a dependent position and not using can also increase swelling in yuour hand. Best advice is to see your doc.
Usually. Generally the hand can swell after arm surgery, especially if the bandage is tight. You should elevate the hand and make sure the bandage is not constricting. If numbness, tingling, loss of pulse or other occur in the hand then you need immediate attention.