I had an abscess under my eye drained 4 weeks ago which was a result of periorbital cellulitis. A doctor 2 weeks ago said the infection was gone, but I still have a hard red lump which they said was scar tissue. Will this go down, or is it permanent?

Use warm compresses . I would recommend to use warm compresses on the lump three times a day for a week. If it did not go away or started to increase in size or have a white or yellow head you need to have it reevaluated. It might be still a collection and might need to be opened again.