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From the history provided here, presence of blood in stools, and possible cuts in the anal opening indicates possible anorectal fissures or mucosal tears associated with chronic constipation. Other possible causes of blood in stools include bacterial or parasitic dysentery, anorectal fistulas, hemorrhoids, polyps, inflammatory bowel disease, ano-rectal abscesses, etc.
You might consider getting yourself examined by your physician. A rectal examination and a stool examination will provide conclusive information for deciding the further treatment.
I hope this helps.