I really don't think your doctor knows what he's talking about. So, in order to give us a clue, you really must get a copy of your results - it's very unlikely your doctor will just tell you. It is your legal right to have a copy under the 1998 Data Protection Act. Post the results on here, and let us have a look at them. But don't forget the ranges! They are most important.
I fail to see how a blood test shows 'brain activity' - but if there were no brain activity, you'd be dead! lol And I very much doubt your doctor does, either. And, in any case, why is that a bad thing?
The thing with lab results when you're taking T3, is that the TSH is likely to be suppressed - at in any case, very low - and your FT4 very low, also. The only important number is the FT3. And, if he failed to test that, then, yes, your results would look very strange. But, that doesn't mean you've 'blown' them! lol
But, he is over-reacting a bit - flexing his medical muscles, I suppose - by telling you to come off it for three months and get tested again. For a start, it will all be out of your system in a week! So, three months is exaggerating. (I think he just wants you to suffer a bit, for having been a naughty girl!). And, besides, he could just look at your results before you started taking T3, to see what your results are like without T3.
If it were me, I would go back and see him with the two propositions I made above, and tell him that he can do what he likes - test your now, or look at your old results - but you intend to go back onto your T3 the next morning, come hell or high water, because you have suffered enough! It's time to stand up to him, and not let him get away with this nonsense! It's not him who has to suffer the consequences of his whims.