Is TSH the only blood test they did? They should also have done Free T3 and Free T4, which are the actual thyroid hormones. If you have those results, please post them, along with reference ranges.
I had shortness of breath, rapid heart rate and palpitations when I was very hypo.
Are you on any medicine?
The heart palpitations are usually sign of hyper not hypo thyroid function.
If you are taking no medicine, I have a wild guess that pressure to the thyroid during the ultrasound damaged some inflamed follicles and caused hormonal leak into the blood stream.