Abby,
Anytime your care team is unable to provide solutions to problems, it is time for a second opinion. You should NEVER be left discouraged or at a loss for what can be done to asddress ANY issue you encounter after surgery. That is the DUTY of the care team.
Call them. Ask - in the strongest terms - if your health is at risk because of the situation. If urine can leak out, and you are wet, bacteria can migrate in - you have an open wound that needs to be cared for. Where drain lines are put in to draw off fluids, the surrounding external tissues MUST be kept dry.
Sensitive skin is another issue - you may be reacting to tape - paper tape is for some less irritating than plastic tape, and some people are sensitive to some of the many forms of tegaderm, a clear plastic film covering that allows inspection of a surgical site with out removing the covering. Again, the care team has options and solutions once you get their attention. barrier creams may help with skin issues.
If a referral is needed, ask the care team for a referral, or follow whatever procedure is necessary to obtain HELPFUL and COMPETENT care. You deserve a recovery without unnecessary stress, pain or complications.
Best,
Jack