Also, if you are not doing well on t4 only, and you can't get him to add t3 in, maybe you could find a doctor that will in your area (there are a lot of resources of lists of doctors who use proper protocol when testing patients)
Some people also do better on natural thyroid hormones such as armour and naturethroid.
Posting your latest labs will help a lot.
Do you have copy of your last lab results? Most likely low FT3.
I raised my dose of synthroid up to 150mcg, but continued to feel hypo. I was putting in a lot of work to be healthy and felt awful. I was always swollen, tired, losing hair, gaining weight ect. After reading up on this forum, I found out that many people need to be on a T3 med. I asked my endo if I could try adding Cytomel(T3med). She agreed to lower my Synthroid and add T3. (2.5mcg twice a day). I've had to push my dr for each increase of T3. I am now on 125mcg sythroid & 7.5mcg Cytomel (twice a day). After giving my body some time to adjust, my symptoms have improved greatly. If you do add T3 make sure you start slowly and give your body plenty of time to adjust to the new dose.
Unfortunately too many doctors only want to go by blood tests. That frequently does not work. TSH is a pituitary hormone that is believed to reflect the levels of the thyroid hormones, but doesn't. I would challenge any doctor to show me scientifically valid data that supports that TSH correlates with either Free T3 or Free T4 (the biologically active thyroid hormones), much less with symptoms.
At best TSH is an indicator, to be considered along with more important indicators such symptoms, and also levels of Free T3 and Free T4. Free T3 is the most important because it largely regulates metabolism and many other body functions. Scientific studies have shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH did not correlate at all.
Another thing nor understood by many doctors is that hypo patients taking large doses of T4, frequently find that their body does not convert adequately the T4 to T3, thus requiring the addition of some T3 for the patient's meds. Also, patients taking T4 meds often find their TSH suppress. this does not automatically mean you are hyper, unless you also have hyper symptoms due to excess Free T3 and Free T4 levels.
So where that leaves you is that you need a good thyroid doctor that will treat you clinically by testing and adjusting Free T3 and Free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels. symptom relief should be all important, not just test results. I think you can get some good insight from this letter written by a good thyroid doctor for patients that he sometimes consults with from a distance. The letter is sent to the PCP of the patient to help guide treatment.
http://hormonerestoration.com/files/ThyroidPMD.pdf
So if you cannot use information like this letter to change your doctor's mind about treatment, then you will have to find a good thyroid doctor.