I was diagnosed with Hashimoto's at 20, and am now 35. I have spent quite a bit of time researching this disease, and have a few suggestions.
As far as medication is concerned, you may have better results with natural desiccated thyroid like Armour or Naturethroid than synthetic thyroid like Synthroid. Both types of medication are prescription only, but because Armour and Naturethroid replace all the thyroid hormones, not just T4 (like Synthoid does) they often have a much greater affect on Hasimoto's patients. I personally feel so much better on Naturethroid, I would never go back to synthetics.
As far as labs are concerned, I think it's important to know where your labs need to be in order for you to feel your best, and have your medication adjusted accordingly. Generally speaking, you will feel your best when your anti-thyroid antibodies are at their lowest, and when your own production of thyroid hormone is suppressed (so, low TSH). Because Hashimoto's is in actuality a disease of the immune system, and the immune system is wired to attack your own thyroid and the hormones it produces, limiting the activity of your thyroid gland can suppress the antibodies that make us feel so tired, achy, foggy-headed, etc. This can be done by taking higher doses of medication (as long as it's safely tolerated).
Find a doctor who listens and have a frank conversation with them about your options.
Most people with autoimmune diseases have a difficult time with dairy and gluten. I really limit these from my diet and have had great results.
Consider an anti-inflammatory diet/regimen. Supplements of B vitamins and vitamin D3, and daily exercise can really help to bring down inflammation, and give energy.
Remember that advice for hypothyroidism probably doesn't apply well to people with Hashimoto's. Things that encourage thyroid activity are not a good idea for Hashimoto's patients because thyroid activity is the thing causing our illness. We generally feel more ill when our thyroid is more active because it causes our immune system to more virulently attack us. That is why some people with Hashimoto's shy away from supplements that encourage thyroid hormone production.
Anyways, this is probably too verbose, but if you think I can help, I'd be more than happy to answer any questions you may have.
Good Luck!