I felt a tear in muscle on anal area while doing dead lift at the gym. now there is a burning sensation inside my rectum. is this serious?

Anal fissures no fun: Anal fissures are like paper-cuts in the anus. They can bleed, hurt, & recur, particularly with defecation & any other activity that increases pelvic pressure. Disorders of anal-rectal function, straining at hard stool, prolonged sitting, heavy lifting, long distance walks/runs are causative & should be addressed. If stool softeners, fiber, topical rx, & behavior changes don't cure, see a surgeon.

Anal fissure??: It is possible that the straining caused an anal fissure. See you doctor for an exam. Many times anal fissures can be treated conservatively. Surgery if conservative measures don't work.