I think your doctor had a very good suggestion. You appear to have a
conversion problem since your FT3 is so low.
Cytomel would most likely make you feel better. T4 is the storage form of the thyroid hormones...your body cannot use it until it is converted to T3. So, FT3 is the most important of the thyroid tests. If it isn't at optimum levels, you will not feel well.
It's always a good idea to have antibodies tested so that you know what you are dealing with...