For anyone suffering with fatigue (associated with thyroid problems or not) I recommend the liquid iron supplement Floradix (includes B12 & Vit C).
I have hyperthyroidism and don't fully understand the links between that and iron absorption problems and vitamin B12, but my doctor tested my Ferritin levels and found them to be too low. I'd heard from my Mum about liquid iron being better than tablets and a friend who recovered from ME agreed, so I gave it a go. It's taken a month or so, but I have so much more energy, it's very exciting.
Apparently even if your Ferritin levels show up fine on a blood test, many ladies (with fatigue) can benefit from taking iron supplements (especially those still having periods). But beware dairy products, wheat, wine and tea can be iron inhibitors too (check by reading iron supplement leaflets) - so even if you take a liquid supplement, try to cut back on the tea etc a bit and make sure you take it before a meal. The tablets require not eating for an hour + either side, it's a lot easier with Floradix (get it at a health food shop), you just take it half an hour before (twice a day).
Iron tablets alone often don't work because a) your body needs a good supply of Vit C and Vit B12 to absorb iron and b) tablet form is less easy to asorb than the liquid form. It can take several months to get your stores of these nutrients up and running. Hope this helps you as much as it's helped me.