Could tegretol start causing breathing problems even after being on it for 5 years?

It's possible: Tegretol can cause many serious adverse effects including aplastic anemia, arrhythmias, and renal disease - any of which could cause shortness of breath. More importantly, there are many causes of shortness of breath besides drug reactions. You need further evaluation. Looking at your meds, i infer that you have CAD - that's a common cause of shortness of breath, even without pain.