You have a lot going on - I have had burn out and it can cause general fatigue.
However you've a few "red flags" too - I'd find out what your thyroid test was just in case and perhaps mention family history. Yes it can mean you're more likely to have it if there's family history. I'd mention it to the gp.
My nails did used to flake but I'm not sure if that was thyroid or other things - since I got in a bit of a pickle with I'll health I now keep on top of vit d, b vitamins and iron and they're much better, plus I'm very careful about managing my thyroid levels.
Hair loss can be either ferritin, vit d, or thyroid. Low thyroid can cause anaemia but also not enough iron can affect how the thyroid makes thyroxine- so it's all a bit chicken and egg. Hypothyroidism has always caused me to become very constipated.
Coeliac disease is autoimmune like most thyroid issues so it can run in families. There's also a slightly higher incidence of hypothyroidism occurring if you have coeliac disease. But you need to keep eating gluten for any tests.
Did they test you for diabetes? You mentioned urinating frequently.
I believe they sometimes treat restless legs by raising ferritin too. I'd make this your priority - don't have dairy, caffeine or calcium near any iron rich foods and eat iron rich foods with orange juice.
Iodine is important for thyroid health; dairy and white fish is the main source. Selenium and iron are the others. To be honest, prenatal vitamins tend to have a good level of what you need there! And see what the gp says about iron tablets. You could boost vitamin d by a bit of sun before putting in cream and you can get high strength sprays from Holland and Barrett (and amazon).