A very minimal introduction of Cytomel T3 or Armour T3/T4 may make a difference - but again I need to side with the above -
You need to get those TSH tests posted.
Yes you definately need to post your lab results with ranges so we can take a look.
T3 therapy is used a lot with thyroid patients with depression and cognitive issues. If not anything ask your doctor for a trial of T3. If he won't go find another dr. Don't put up with being dismissed when you are the one suffering. I made that mistake. I made the switch to Armour and am increasingly feeling better and better. I ended up having a conversion problem that my old endo never tested for. If he had bothered to listen and test my free t3 he would have seen this. He is narrow minded regarding T4 meds only. I made the switch and have no regrets! My health is what matters not his ego! I wasted 2 yrs putting up with crappy treatment.
I think you should post your numbers. TSH, Free T3 & Free T4. If your doc has upped your Synthroid and you have felt jumpy... T3, unless meticulously adjusted, will do the same, possibly more so. Also you mention that they've found a nodule on the remaining half of your thyroid. If it were me... I would take care of that issue first. Protocol is that if cancer is found in your thyroid, the entire thing comes out for the very reason you're describing now. The odds are that the other half was bound to have problems at some point in the future. After the nodule is taken care of, and your numbers are reviewed, if your T3 is low and T4 a little high, I'd definately ask for a combo therapy. But you'll probably have to find a doc with an open mind or ask for Armour.