Hangnail pulled then infection 2 weeks. got better and now same type pain, slight swelling, pink. applied neosporin 2 wks, againn now. not improving. ?

Paronychia: It sounds like you may have a paronychia, which is an infection of the skin around the edge of a nail. Sometimes you can see a collection of pus next to the nail; sometimes it's just red and painful. A doctor can drain these with a very simple procedure. Sometimes you need antibiotics. See your doctor, a hand specialist, or urgent care for evaluation and treatment if you worsen/don't get better.