Neurological symtoms and dizziness can be caused by hypothyroidism. I have had them for ages before my bloods caught up and went out of range (along with lots of other symptoms. . I have been taking levo for just over two weeks and have seen an improvement in last couple of days.
Are you taking any b vitamins. I was caught out a few weeks ago as I didn't stop my b supplement and it altered my TSH and T4 test I had. Luckily my GP agreed to retest so we are clear or off that the b complex affected the result. Any supplements containing biotin should by stopped 4/5 days before thyroid testing.
As a precaution, I now stop all b vitamins a week before and my other suppements 3-5 days before as I can't cope with the leg cramps when I'm not taking magnesium for too long.
Will add a reminder to my diary for also stopping levo on the morning of these test.
If you've been taking biotin I would dmstingly recommend rearranging the test for he end of the week at least to give time for it to be out of your system. I was taking low dises and it brought all my results in range (when they weren't). At higher doses people have been misdiagnosed with graves. Or presumbabkg had medication adjusted based on false results.