Do you know if the doctor you're seeing in January is willing to test Free T3 and Free T4? Not all endos will do so as some think TSH is enough.
Well, shame on your doctor for not telling you that you shouldn't take iron at the same time you take your synthroid. Are you taking anything else at the same time? You should be taking your synthroid first thing in the morning, with water, only and nothing else. All supplements, particularly, calcium, magnesium, iron, etc should be separated from thyroid med by, at 4 hours.
It's no wonder you have a hard time getting number normal, if TSH is the on thing they ever test... again, get a second opinion.
You need to be getting Free T3 and Free T4 tested every time you have a TSH test. Those are the actual thyroid hormones and correlate much better with symptoms than TSH, with Free T3 correlating best, as it's the one that's used by every cell in your body.
It's not good enough just to get the numbers normal... you have to alleviate symptoms as well.
What, if any, symptoms do you have?
Get a second opinion... if you have a parathyroid issue, it needs to be taken care of. Have you had thyroid and parathyroid blood tests done? If so, please post them, so we can see what your actual levels are... Be sure to include reference ranges, as those vary lab to lab and have to come from your own lab report.