After only 4 months on Levo it doesn't surprise me that your dose is still changing. I'm not impressed that the lab is doing some patient blaming to explain the results though. Also, since you have autoimmune thyroid disease your thyroid function test results will inevitably fluctuate.
If you have an antibody attack on your thyroid you may start showing results with a low TSH and a higher FT4 and FT3, possibly making you feel hyperthyroid (i.e. overactive). Your doctor will tell you that you are over-treated and will reduce your levo. When the antibody attack subsides your TSH will rise, your FT4 and FT3 will drop, and if you get tested your doctor will tell you that you need an increase in your levo. There may well be more patient-blaming going on as well.
The way to reduce these problems is to try and reduce the antibody attacks on your thyroid. Your treatment will fluctuate less, giving you some stability and making you feel better.
Are you on a gluten-free diet? If you aren't, then it is recommended by patients that you go gluten-free - and it has to be 100%. You can't be a little bit gluten-free. It is all or nothing.
For more info on autoimmune thyroid disease, take a look at these sites :
By the way, the reason that an autoimmune attack on the thyroid changes your thyroid function test results is that as the cells of the thyroid are killed off they release their load of thyroid hormone into the body/blood stream.