I have shortness of breath. I do not smoke. I do havr hypothyroidism. Can it be related?

Not likely related. It is not likely to be related to hypothyroidism.You need to get checked by your doctor or a pulmonary specialist, you will need examination and if indicated pulmonary function test and/or xrays etc to make a diagnosis.There can be pulmonary and cardiac causes of shortness of breath even in non smokers.If no cause is found in lungs than get a cardiovascular evaluation and tests including ekg/echoca.