After several months of having the upper ear cartilage pierced it still hurts. Is there supposed to be a small dent where the stud has been?

Pain and discomfort are part and parcel of getting the cartilage pierced with a piercing gun. The piercing gun user knows that they are not allowed to pierce ear cartilage with a piercing gun. Properly done cartilage piercing done by a professional body piercer would have been healed by now. The swelling is due to the stud backing being too close to the skin and not allowing the piercing to drain or breath properly.