Small scab on upper lip, won't go?

Um hi, so I've had this very tiny scab on my top lip for a few months now and it won't go away, it doesn't itch and it doesn't bleed and nothing comes out of it, but when it hurts when I try to pick it and basically won't remove itself. It is raised and I can feel the bump when I touch it. I googled it and it said it might be a coldsore scab but in which case why hasn't it gone away after this long? There are literally no other symptoms other than it being there and it's very small so I doubt its anything serious, but it's bloody annoying... would anybody advise seeing a doctor about this? Thanks!