Despite the numerous negative effects, cigarette smoking has a protective role against some autoimmune and inflammatory disorders. People who quit smoking are 6 times more likely to develop Hashimoto’s thyroiditis (most common cause of hypothyroidism in developed countries). This autoimmune disease is genetic which is why thyroid diseases run in families. If you want to test for Hashimoto's thyroiditis ask your doctor for the following tests: thyroid peroxidise antibodies (TPOAb) and thyroglobulin antibodies (TgAb).
First thing to realize is that TSH is a pituitary hormone, not a thyroid hormone. Doctors like to think that TSH is a good indictor of thyroid status, but in reality it is affected by so many things that it has negligible correlation with thyroid status, for which the simplest definition is "T-3 effect in tissues of the body". TSH even has a weak correlation with the biologically active thyroid hormones, Free T4 and Free T3. The best indicator of thyroid status is symptoms, followed by levels of Free T4 and Free T3. There are other important variables, but those are a good start in evaluating a possible hypothyroid patient.
So please look at this link that lists 26 of the most typical hypothyroid symptoms and see if you have any that you may have overlooked. Note that there is a much longer list that even includes ADHD, although usually thought to be more of a symptom of hyperthyroid.
http://endocrine-system.emedtv.com/hypothyroidism/hypothyroidism-symptoms-and-signs.html
If you have been tested beyond just TSH, please list results and reference ranges shown on the lab report. If not, with your high TSH result, I think you need to request to be tested for Free T4, Free T3, Reverse T3, Thyroid Peroxidase antibodies (TPO ab), Thyroglobulin antibodies (TG ab), cortisol, Vitamin D, B12 and ferritin. Do you think you could get those done? If you have any questions about the need for these, please read at least the first two pages of the following link, and more, if you want to get into the discussion and scientific evidence for all all that is recommended. Note especially Sugg. 4 on page 2.
http://www.thyroiduk.org/tuk/TUK_PDFs/The%20Diagnosis%20and%20Treatment%20of%20Hypothyroidism%20%20August%202017%20%20Update.pdf
You mentioned your family having thyroid issues. Based on extensive experience, I expect that the likelihood of their being adequately diagnosed and treated is fairly low, so they might also benefit from reading the last link.