I'm not sure - I've was dx with Hypothyroidism 4 years ago. All I know is that on the blood testing order form, I think it just called for a TSH Test. I think this covers TSH, T3 and T4 testing?
Here's a website I found that covers Thyroid testing:
Thyroid Testing
It seems odd that all 3 tests would show up a false negative, but it can't hurt to have a 4th test.
I only get tested a few times a year usually, but now that I'm pregnant - i will get tested more often. Was tested at the start of my PG, will be tested next week at 21 weeks and then some more times, but not sure when.
Good Luck!