The DMSO may be what is causing you to burn. The DMSO cocktail helped my IC even though I burned for a while afterwards. The benefits out weighed the discomfort. That was my own experience; it could be different for you. Your doctor should be the one to help you with health care decisions. He can isolate the ingredients in the DMSO cocktail and help you locate which one is causing your problems.
No, I never reuse catheters without sterilizing them--per doctors orders. Discuss sterilizing techniques with your doctor.