Hello,
Burning oozing mucus from the rectum is characteristic of proctitis(an inflammation of the anus and the lining of the rectum) and rectal prolapse(the walls of the rectum protrude through the anus) but other conditions like ulcerative colitis and inflammatory bowel disease, irritable bowel syndrome , Bacterial infections, such as those from Campylobacter, Salmonella, Shigella, and
Yersinia and intussusception(telescoping of a part of intestine on the other) can also cause them.