A painful lump outside the anus that has appeared suddenly certainly sounds like a thrombosed hemorrhoid, that is, a hemorrhoid that has a small blood clot inside it (a very common and painful problem!). If small (ie around a cm or less) these are treated conservatively with warm Epsom salt baths and topical hemorrhoid creams. If much larger and very painful, your doctor may need to perform a small surgery to remove the clot. It's not as bad as it sounds (trust me!) and you would feel much better afterwards.