My understanding is that the blood test results from the lab will show what's considered an acceptable range for TSH levels. I did some research on the net and it sounds like there is some differing opinions on what "normal" is. My lab results stated the range was .5 to 5.0. My TSH was 5.5 Just slightly out of range. I also never had any symptoms but the numbers are the numbers. Based on my reading of the FAA med regulations, I felt compelled to ground myself and seek medication to put my TSH level into the normal range. (Synthroid does require a waiver/special issuance). Unfortunately, it took about 4 months and some prodding from my AME to get the paperwork approved. It's a simple waiver that many people have and should be no big deal. Bear in mind this is for a first class.
To the OP, I'd suggest you find out specifically what the limits that were on the blood test paperwork. If they are .05-5.0, like mine are, than you are within limits at 4.51. If you are outside the stated limits, then it's my opinion that you aren't qualified to hold a medical until you are within limits. That was my take after reading up on it and was also my AME's opinion and the opinion of our union's medical advisor. Perhaps there are some gray areas in the regs I'm not aware of. Not sure if your doctor was also your AME but I know my regular doctor knows nothing about FAA rules besides what I told her. She couldn't believe what a cluster was created by a slightly out of range TSH level and putting me on the minimal available dose of Synthroid.
I think the rise in my blood pressure dealing with the FAA was much worse to my health than being .5 outside the range on TSH level. But i digress.....