Can you tell me what tests they did to rule out Hashimoto's? And do you have the actual results, with reference ranges?
Do you know if the T4 test that was done was a Free T4 or a Total T4? Those aren't the same tests and don't provide the same information. Typically, when we see "T4", we assume it's Total T4, which is considered obsolete and of little value; however, the result of yours, is one we, often, see for Free T4. Do you have the reference range for it? Ranges vary from lab to lab and have to come from your own report.
It's always a good idea to get/keep copies of all lab and diagnostic reports for your own records, so you'll have them for future reference...
First off, if your thyroid was swollen, that means you had a goiter... something was causing it to be that way - so it wasn't completely okay, even though it might have been functioning properly at the time.
Secondly, since there was never a Free T3 test done, you aren't completely sure that it was functioning properly. Free T3 is the hormone that's used by all the cells in the body. Free T4 is a storage hormone and must be converted to the usable Free T3; not all of us adequately make that conversion.
Studies have shown that selenium can help with the conversion of Free T4 to Free T3... Iodine is not, typically, recommended, except under the supervision of a doctor, especially, if you have Hashimoto's as it can make the autoimmune reaction that much worse. Since you had a swollen thyroid, which is often caused by thyroiditis, you may have an autoimmune issue.
L-Tyrosine is used, along with iodine, in the production of thyroid hormones... if you're already producing excess thyroid hormones, both iodine and L-tyrosine would counter-productive.
Zinc should be taken with Copper in order to keep the 2 in balance... you should talk to your doctor before starting new supplements. You can get a micro-nutrient test to determine if you have deficiencies...
The first thing your doctor did wrong was put you on a thyroid medication based only on a TSH reading, if that what he did... were there ever any Free T4 and Free T3 tests done? Those are the actual thyroid hormones, whereas TSH is a pituitary hormone, which is a diagnostic tool, at best; it should never be used as the sole factor in prescribing thyroid hormones... If you have results for Free T4 and Free T3, please post them, along with their reference ranges, since ranges vary from lab to lab and have to come from your own reports.
That said, because synthroid has a long half life, it would take 4-6 weeks for it to be out of your system after stopping it. It could take a short period of time for your own thyroid to kick back in, but not 10 months.
Did any of these doctors, by any chance, do any antibody tests to determine if you might have Hashimoto's? Since a TSH of 5 is, technically, hypothyroid, it would seem prudent to find out WHY you were hypo, even if you might not have had symptoms at that time.
If there were any other relevant tests done, please post them, along with reference ranges.