During my bowel movement, i feel a muscle(?) come out temporarily and then after i defecate, i feel it retract in. i see a moist flap of skin on anus.

Rectal prolapse?: Anal/rectal pain and swelling may be an indication of underlying disease--fissure, proctitis, fistula, abscess. Hemorrhoids may be exacerbated by increased pelvic congestion. Rectal prolapse is a outward bulging. Anal trauma of any kind may cause mechanical injury. Evaluation is recommended to distinguish serious versus less concerning reasons for your symptom/sign as described.