First, to my knowledge, there is no relationship between thyroid hormone and airway inflammation or obstruction. The excess doses you took could easily result in a hyper-metabolic state that would increase oxygen consumption and, secondarily, increase the work of breathing to provide the oxygen, that would result in increased shortness of breath. That might have been true when you overdosed, but, thyroid has a short metabolic half life and the excess thyroid is long ago, out of your body. Further evidence of that is the normal TSH, T3 and T4. So, if that thyroid is having any effect now, which is very unlikely, it would have to be some indirect effect or toxicity that somehow harmed another organ, that remains injured although the excess thyroid that caused it is gone, and altered your body physiology. That is a real possibility.
The most likely explanation for your persistent symptoms is that your COPD and/or bronchiectasis have worsened. However, it is equally plausible that your symptoms are not related to lung function, but rather to occult heart disease, caused by the high doses of thyroid. Excess thyroid hormone is usually the result of over-activity of the thyroid gland but the end result on one’s body and organs is the same if the excess level is caused by toxic dose ingestion. The effects of increased levels of thyroid hormone on the heart and blood vessels is well known, and this includes its causing what is called “high output” heart failure, along with a weakening of the heart called toxic cardiomyopathy. That is a disease of the heart muscle, resulting in heart failure. If you have continued to have a high pulse, that could either be a sign of or a cause of heart failure
I suggest that you show this message to your doctor and ask if he/she might want to check-out your heart for evidence of heart failure.
To summarize, your doctors may want to reevaluate your COPD, bronchiectasis and your heart function. Please let us know how things go.
Good luck