The TSH will vary naturally depending on the time of day that the blood was taken, it will be lower in the morning and higher in the afternoon, so if the variation is due to different blood test times, then it would not be anything to worry about. If, on the other hand, it were an upward trend every time the blood is taken, it could be an indication of reducing thyroid function.
For many people, a TSH of 1 point something would be perfectly normal, or even higher. But for me, that level would be too high. I had a TSH of 1.4 in December and I was unable to function on any level, my heart was enlarged and I was getting palpitations, and my cholesterol was 9.7. I had breathing problems, balance problems, constant pain and almost permanent exhaustion, insomnia, hair loss and skin rashes. I was unable to fight infections and had an almost constant cough.
Almost nine months on, my TSH is 0.03 and I am a different person. I am pain free, my cholesterol had fallen to below 7 in June (my next test is due shortly), I have not used either of my inhalers for over six months, I am sleeping better most of the time, I have lost a stone in weight, I am more active, I can get through the day without falling asleep as soon as I sit down, even my face has changed shape. I now recognise myself in the mirror!
What this shows is that the actual 'normal' TSH can vary from person to person, there are some on this forum who are well with a TSH over 2, and then some like me who are only well with a TSH of well below 1.
It seems a good idea to get B12 and folate and ferritin plus vitamin D checked, it all can contribute to feeling unwell. If all these are fine and you are still unwell, then the doc needs to look further. I do hope that you can get to the bottom of this vertigo problem, it's horrible. Have you had your ears looked at, just to see they are OK?
You do not say if you have any other signs or symptoms which could indicate low thyroid, what led your GP to test thyroid levels in the first place?