Wouldn't let me post below that link!
This is the best charity for a newly diagnosed person imho. It's the official charity working under the thyroid association of endocrinologists.
I would digest all the info in these two before looking elsewhere on the Internet tbh; there's a lot of quackery and also certain trends among the thyroid community mainly as it is hard to get on top of feeling well, but it is doable.
Key thing to understand is that getting well (or getting ill) can take a long time. I've recently been reminded after a phase of hypothyroidism, as thyroxine has a long half life (around 7 days) it takes a good 6 weeks or more to reach correct levels and it then takes another 4-6 weeks for symptoms to begin to improve.
You are likely to need to adjust your dose after a blood test after starting the 100, 6-8 weeks is best and keep going really till TSH is ideally around 1 or just below and then see how you feel for a good few months. Be mindful of this and find out results as some gps accept 2.5 as ok; generally (as the bmj book says people need to be around 1.)
I developed horrendous constipation when underactive and I know if I'm balanced actually via my gut often. Overactive can cause diarrhea. I had to cut out museli and brown rice and eat well cooked porridge and apples to help till it eased.
You shouldn't need to do anything other than take your thyroxine regularly. Consistency is key with thyroxine. As much as possibly 30 mins or more away from food and other drinks. Read the leaflet carefully as a lot interferes with it.
Other levels that may affect how you feel are ferritin (iron), over 70 is best, vit d, vit b12 and folate. Find out if these have been tested; if not and if after you've got your levels well controlled and still have some issues with fatigue, ask to get these checked. Iron can drop a lot with hypothyroidism so it's worth checking.
Regarding diet just eat healthily, slightly lower carbs perhaps, lots of protein and iron rich. for best iron absorption, you could try making sure iron rich foods are eaten with orange juice and not within and hour or more of anything with calcium in it or milk.
Soya can interfere with absorption, really good info here: www.btf-thyroid.org/thyroid-and-diet-factsheet
Selenium is also really important for conversion of thyroxine (t4, technically a prohormone) to t3 which is the active form of the hormone.
I recently read a paper that hair loss won't correct until zinc levels are optimum. I used to take berocca for b vits but you'd need to take vit d separately as it isn't included. At the mo I'm taking a breastfeeding multivitamin tablet and an extra vit c and zinc fizzy tablet when I remember (as am bfing).
I wouldn't start investigating things like gluten unless you notice a big difference if you avoid for a week or so as so many of your symptoms could be thyroid based and could take a while to go away.
FWIW, when you are well, exercise and strength building exercise is really important. You will find it incredibly hard to do until levels are good and it will take a while for you to be able to do much so pace very carefully. But it actually makes a difference to the whole system, possibly boosting conversion of t4. Muscles can waste in either hypo in hyper thyroidism so keeping strong is very important.