Apply a warm washcloth to the area so the hair can be removed easily. Use tweezers to remove the hair from the follicle. Clean and treat any remaining infection.
Start exfoliating your face before you shave. Don't use any product with alcohol in it. Using products that have azulene and witch hazel will reduce the redness and swelling.
Use warm wet compresses several times a day. When the hair looks 'ready' take a pair of tweezers and pull the hair straight out. Apply an antiseptic. Rarely does an ingrown hair cause a serious problem.
My husband often has this happen because he shaves so often. He uses tweezers to pull the hair out. Sometimes if it is hard to get I have to help him. It has worked every time.
Try to lift the ingrown end out with a pair of tweezers, but do not pluck the hair out. You could also use products that contain azulene, allantoin, and witch hazel. Those will help reduce the redness and swelling.