If you have been clinically diagnosed as being hypothyroid then it is not a good idea to stop your medication. Your body needs it to function normally or you will develop more serious health issues. It sounds like you need to find a medical practitioner that is willing to work with you. An endo is not the only option (if you only have one in your area) so try consulting with a general physician or nurse practitioner. Explain your situation and see how they respond - it's worth a try. If you can share your recent lab results with reference ranges, we can offer some insights. Good luck!
Do you know the cause of your hypothyroidism? Typically, once we're diagnosed, we need medication for life. Thyroid hormones control our metabolism, heart rate and other body systems. Without adequate hormones our entire body will slow down.
It sounds like your doctor is only testing TSH, not the actual thyroid hormones, Free T4 and Free T3? If you've had those tested, please post the latest results, along with the corresponding reference ranges. TSH is pretty immaterial when it comes to managing replacement medication. We have to go by the actual hormone levels.
If you can let us know where you live, someone might know of a good thyroid doctor in your area. If you prefer not to post your location here, you can send it to me via private message.