Having shapeless flaps or lumps of flesh usually found at the anal verge is an extremely common condition, known as having anal skin tags.
Anal skin tags are often found in conjunction with other anorectal disorders or problems (appear due to an anorectal injury, trauma, or inflammatory lesion).
Infections (the practice of wiping the perianal area with toilet paper normally fails to completely cleanse the perianal area of residual fecal matter, some of which remains on the surface, causing irritation with itching and burning sensation and can give rise to skin infections or other skin disorders) and inflammations are associated with pain, discomfort and tenderness.
This bump could be also a genital wart, caused by HPV, and if that's the case, you should be performed a complete genital and anorectal examination to detect additional growths.
Remember, that having benign growth around anus, doesn't excluded the option for having additional growths and lesion with more serious nature in your anal canal.
So, it will be good for you to get medical attention.
Did you have external hemorrhoids weeks before noticing this skin bump?
Have you experienced anal injury recently?