There is an assumption that T3 medications cannot be prescribed in the UK currently. Liothyrine is classified as 'Amber' under the UK prescribing guidelines.
http://www.bnssgformulary.nhs.uk/Format-of-the-Formulary-and-Traffic-Light-Clasifications/
My GP said she didn't think she could prescribe a T3 med, nor did she think I could be having a problem on it. She then checked and found that, according to the prescribing guidelines, a GP can take over the prescribing, once a consultant had got me established on it (sorry I'm struggling with words here). I'm lucky that my GP is quite open minded and she agreed to refer me to the consultant I found. If he agrees to trial it, my GP will prescribe.
I too have had flashes of normal since starting on levothyroxine. Every time my dose increased I got a day or two of normal, but it doesn't last, and when I try and explain that to doctors they look at me as if I'm very stupid. I wonder whether there is some hormonal imbalance at play in ME/CFS which involves more than just the thyroid.
Thyroid UK has a list of sympathetic NHS consultants with notes on whether they will trial T3. If you can get your GP to refer you to a local consultant, then you are in a much safer place than self medicating.