Good questions for the doctor.
Following is a link to some useful info on nodules.
https://www.endocrineweb.com/conditions/thyroid-nodules/thyroid-nodules-prevalence-symptoms-causes-diagnosis-treatments
There is an association between Hashi's and nodules, but not all Hashi's patients have nodules. Have a look at this info.
https://www.ncbi.nlm.nih.gov/pubmed/3605864
First thing to understand is that hypothyroidism is not, as usually assumed, just inadequate thyroid hormone. Instead, it is"insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to, thyroid hormone". So it is not just thyroid hormone, but the body's response to it, which is affected by a number of body processes and variables. And TISSUE T3 EFFECT determines your thyroid status.
Due to the number of processes and variables TSH has only a negligible correlation and Free T4 and Free T# have only weak correlations with TISSUE T3 EFFECT. So there is no direct measure of TISSUE T3 EFFECT. Instead we are left with indirect measures, of which the most important is signs/symptoms that occur more frequently with hypothyroidism, followed by expanded biochemical tests to support clinical findings.
You have a number of symptoms that can be related to hypothyroidism. You have only limited test results to date. Those don't really reveal much. You need to get your doctor to test for Free T3, Reverse T3, cortisol, Vitamin D, B12 and ferritin, in order to have a better understanding of what is going on. Also, it would be good to test for TPO ab and TG ab, as suggested by Red_Star.
If you will get those done and then post results and reference ranges we will be glad to help interpret and advise further. If you want to confirm what I have said, click on my name and then scroll down to my Journal and read at least the one page overview of a paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective.
For diagnosis, evaluation of symptoms is even more important than blood test results. Please tell us about any symptoms you have.
Not sure of your reference range for free T4.