Your experience of constipation
& tight anal sphincter has nothing to do with your disc slip.
If in any case your disc slips further causing cauda equina compression (part of spine that controls the urination & bowel movement) you would experience loose bowels or incontinence
of urine (inability to control both of them).
But for your information prolonged constipation causes increased pressure on the discs while evacuation bowel. So, I would advise you to get rid of constpation as soon as possible.
Orthopaedic & Neurological
Lifestyle Medicine Counsellor