swell on entrance to the anus

Hemorrhoids can be thought of as a weakening in the tissue supporting/surrounding the blood vessel.  Therefore, these blood vessels can pooch out when one applies underlying pressure.  When this weakness is in the colon leading to little outpouchings, we describe that as diverticulosis, which when inflamed & infected is called diverticulitis.  But I digress.  Getting back to the hemorrhoids, every time someone has a constipated bowel movement, where by s/he has to strain hard, that person is applying significant pressure to the anal region.  Over time, this increase in internal (abdominal) pressure can lead to weakness in the tissue around the anus.  At this point, the blood vessels in the area can pooch out and enlarge.  This visible enlargement is known as a hemorrhoid.  Of course, it's more prominent after defecation which requires a lot of pressure.  But if you're lucky, once that pressure has been lowered, the blood vessel (hemorrhoid) can revert to normal and not remain prominent.  The hemorrhoid is most likely bluish/black due to the venous blood in the vessel.  It's less like to be painful if it's an internal hemorrhoid.  Non-thrombosed external hemorrhoids aren't painful either.  However, if a clot has formed in the hemorrhiod, then it can be quite painful.  But this is all just a wild guess.  Best for you to go see your family physician to be absolutely sure nothing dangerous is going on.  Good luck!