It sounds like hemmeroids to me. They can look like a fleshy ball or buble outside the rectum and if they are thrombosed they can be purple, large and very painful. Constipation and pushing will cause them to bulge.
They can be pushed back in and they burn, itch and throb. Hot baths with epsoms salts as often as possible. Soak a cotton ball in witch hazel and leave in on the area as long as possible. With hemmeroids the more time on your feet the more they hurt, try to put your feet up. If you can wear support stockings they help for the vericose veins that cause hemmeroids. Metamucil should be taken daily to add fiber and help pass the stools. Lubricate the rectum with vaseline or vit e to help the stools slip out without irritating the hemmeroid.