I remember your earlier post in which you talked about the swelling in your throat, and the doctors suggest it's from reflux disease. If the only test you had was total T4, (which would have the lab range you mention) that isn't enough testing to diagnose a thyroid problem. Have you had a complete thyroid panel done? If not, you should. If you have, post your results here, and someone will be able to interpret them.
My doctor also misdiagnosed my symptoms as gastric reflux. It was only through my persistence that he did a basic TSH test (only TSH... not a full panel). I took that test result to an endocrinologist who diagnosed my Hashi-hypo disease.
"We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses." Abraham Lincoln