I am hypothyroid too, I was fit, strong, and slim, couldnt keep the weight on and couldn't stop moving. Then suddenly I was tired all the time and getting odd symptoms. After 2 years of going to the GP and being told I was just getting older (in my early 30s), I started to gain weight super fast, 4st in 4 months eating nothing but salad without dressing. 2 Friends suggested getting a thyroid test, GP told me I could waste my time if I wanted and gave me a form. A couple of hours after the blood test I got a message from the GP saying it was urgent that I came in. Then found out the the NHS have no idea what to do with thyroid patients and levothyroxine doesn't suit me, one of it's side effects can be weight gain. hurrah! But they won't give me a prescription for me to try a natural source of thyroxine like Armour even though I would be paying full whack for it 😡
After a lot of issues with GP I asked to see our local Endocrine consultant as a PP suggested above. He told me that all thyroid patients should see the local consultant and was horrified to find it took 10 years for me to get an appointment with him because the GPs wouldn't refer. He upped the dose and told me the GPs will fiddle with the dosage all the time if I let them, he was right there.
My suggestion is like the PP who suggested her getting a second opinion from the endo consultant, they will run a barrage of tests which the GPs will not. Your friend is entitled to an appointment with one and she may prefer to see the consultant several times, the GPs should refer her any time she asks.
There are suppliments that Thyroid UK and other supposedly knowledgable sources will tell you are rubbish but then they also used to say that eating goitrogenic foods like soya and cabbage is fine until everyone else in the world said it wasn't. I recently started taking NAC for my liver but it's had quite a positive effect on me so far in many things not least my hair and skin being so much better. I'm considering Ashwaganda, there are loads of suppliments that will help with the symptoms your friend has but we are all different so when your friend is on a better dose of thyroxine and is more settled then she can look at her symptoms and see what can help her get through the day. Don't expect to go back to the old person with treatment, I don't recognise myself physically or mentally, it's not all bad though, although I'm still not a relaxing person to be around, I'm way more relaxed and sedentary than I was
Oh and for some history about thyroid treatment in the western world, have a look at Ray Peat, he has some interesting snippets. Might not be immediately helpful though so that one is at your leisure!
Lastly, you may already know this but in case you don't, thyroxine is one of the scripts that you can get a free prescription card for. Whatever anyones opinion is on the fairness of that, it's available if your friend wants to apply.