Do you have current thyroid blood test results? If so, please
post them, so we can see what your levels actually are. Be sure to include reference ranges, since ranges vary lab to lab and must come from your own lab report.
Are you currently on a thyroid replacement medication? If so, which one, at what dosage, and how long have you been on it?
Even though shortness of breath can be a hypo symptom (or any other possible heart related symptom) should be checked out by your doctor.