Can you get a rash on your body due to constipation?

Not "due" to it. Constipation does not cause a rash. A person can have both a rash and constipation, just as a coincidence, or due to a disorder that causes the constipation and the rash. Some medications cause constipation, and one can have a rash if allergic to the same medication. Some people with thyroid hormone imbalances get constipation and rashes. A primary care doctor can help figure things out.
Constipation. Dermatitis herpetiformis is an itchy, blistering skin disease that also associated with gluten intolerance. Rashes usually occur on the elbows, knees and buttocks. Dermatitis herpetiformis can also cause significant intestinal damage identical to that of celiac disease. Dermatitis herpetiformis may also be entirely free of noticeable digestive symptoms. No specific skin rashes from constipation.