I bought a new to me TT that is in really great shape and had very few areas of de-lamination. I noticed that the dealer the folks I bought it from who they got the unit from a year ago, went over it ...
I'd have a pressure test done to find the exact locations of your leaks and correct them from there. There's no point of fixing part of the problem. I'd try to get any leaks corrected ASAP to avoid additional damage. I would also consider opening the inside of the swelling wall to evaluate damage and at least give it a chance to dry.