There are a couple possible situations that could be causing your symptoms. Unfortunately, all of them require being evaluated by a physician. Futhermore, you can have a combination of each of them.
Hypothyroidism is a very common disorder that is fairly easy to treat, but it has significant long term and short terms effects on the body.
1) You are being under-treated with thyroid medication. You should return to your
primary care physician to be evaluated with routine screening blood work.
2) Your hypothyroidism caused significant cardiac damage. Generally, people can get decreased contractility of the heart muscle, decreased
heart rate, and increase resistant in the vasculature which results in an overall decrease in the amount of blood that can be ejected from the heart with each beat. In some people this can be short term effect, while in others it can a long term effect. You should see a cardiology so you can have an
ultrasound of your heart.
3) You can have significant volume overload from many different causes, one of them being hypothyroidism. You will need to see a doctor to be evaluated and putting on medication that will help decrease the amount of volume.
4) You could have an unrelated heart or lung condition effecting your
shortness of breath. You will need a chest x-ray and some routine screening blood work to evaluate both.
There is no simple answer. You ultimately need a full work up to ensure that your heart, lungs, and thyroid are in good health.