I often feel like I tear something when having a bowel movement and bleed out. Is this something to worry about?

Anal fissure? Anal fissure is a tear in lining of anus; can be associated with hard stool, tight sphincter; can become chronic. Can be rx'd with meds, including antispasm rx; sometimes can need surgery. Need to get checked that there is nothing else going on, like a tumor. See your doc, or GI md, or colorectal surgeon.