If you want to have the best possible chance to get the tests and diagnosis and treatment you need, I highly recommend you read the first two pages of the following link, and more, if you want to get into the discussion and scientific evidence for all that is recommended. You might even consider taking a copy of the link with you and if the doctor resists doing what you need, then give him the paper and ask him to read and reconsider your diagnosis and treatment.
http://www.thyroiduk.org/tuk/TUK_PDFs/The%20Diagnosis%20and%20Treatment%20of%20Hypothyroidism%20%20August%202017%20%20Update.pdf
Please let us know how the appointment goes, and we will be happy to advise further.
all your symptoms are consistent with hypo. add to it your family history and to top it off your BELOW range FT4 level. And I would call that a trifecta. You are Hypo and would probably benefit from beginning thyroid replacement therapy.
The fact that you have been low for a long time suggest that your Dr has "immaculate TSH belief".
You may try to convince your Dr to attempt to give a clinical trial of a starter dose of T4 medication such as Synthroid. if the Dr resists, you will need to find a new doctor. Unfortuately, most Dr's are essentially taught TSH belief. And you will be in the hard place so many of us find ourselves in. Suffering needlessly because of Doctors inability to truly understand how to effectively treat thyroid issues.
when were your last blood tests? And were you ever tested for Free T3?
If it has been some time since your last blood tests, and/or you were no t tested for Free T3, then I would recommend you get new tests and demand Free T4 and Free T3 are both tested.
In addition you may also want to have the following levels tested which are commonly low and some having similar symptoms as low thyroid.
1) Vitamin D3
2) Vitamin B-12
3) Iron
4) Ferritin
Contrary to what most doctors believe, in trying to assess a person's thyroid status, symptoms are far more important then lab test results. So, before discussing any lab results we need to know what, if any, symptoms you have.