Thank you for your query at DoctorSpring.com.
Although you do have certain symptoms which may suggest hypothyroidism, the biochemical tests are absolutely normal.
Symptoms in thyroid diseases are often non-specific and eventually it is the blood test for TSH and T4, T3 which leads to a diagnosis of hypothyroidism. So you do not have any thyroid dysfunction.
You can be rest assured that these symptoms are not due to a thyroid problem. You can repeat the test after 1-2 months if symptoms persist.
The dizziness seems to be migranous vertigo as your doctor has mentioned. The other symptoms like breathlessness, chest tightness etc need to be evaluated with a physical examination of all systems and a basic work-up. So please consult your physician in this regard.
I hope this was helpful. Feel free to discuss further.