I am hypothyroid as well. I have heard that exercise intolerance can be a symptom of it but my understanding is that you would only have exercise intolerance if your thyroid numbers were not in line.
I have experienced some of it in the past but honestly since my numbers are in a good spot now from the medication, I fell like I can do anything exercise-wise.
Perhaps your blood work needs to be reviewed or your medication needs to be increased. Best wishes - I know this condition sucks!