I recently had an implant. today the dentist unscrew something and performed a cleaning, then screw it back again. two hours later the pain is awful.

Hard to tell: Typically implant restoration does not cause pain. If you have a single implant/crown restoration, it was unscrewed & removed to clean the area, pain might occur if the restoration was mis-aligned on re-seating. If it is a multiple implant restoration, possible mis-alignment of a section, but hard to determine anything without examination. Contact your dentist immediately for an evaluation.

Impingement: I agree with dr. Gordon´s thorough and excellent answer. Another thought is that the implant was well below the gum line and the gum is sore all around the implant from a deep and thorough curettage of the area.