Are those Total T4 andTotal T3, or Free T4 and Free T3? Also, please be aware that just having T3 and T4 within the range does not mean that all is well. Please tell us about any symptoms you have. That is more important than test results. Also, if you will please post your test results and reference ranges, along with symptoms, we can give you an opinion of your status.
Vitamin D needs to be at least 50. B12 needs to be in the upper end of its range, and ferritin should be 70-100. If not tested for ferritin, you should make sure to do so and then supplement with a good form of iron to optimize.
If you want a better understanding of all this, I highly recommend reading at least the first two pages of the following link.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
I assume you are taking Thyronorm due to hypothyroidism. Thyroid hormone is used by all the cells of the body to maintain adequate body functions. Your thyroid med is necessary to maintain adequate levels of thyroid hormone, and it is unhealthy to go without.
Certainly you could stop the Thyronorm, but I think a fast is intended to show commitment and belief, without doing harm to your body. For that reason you will be taking fruits, milk, water, etc. In my opinion your Thyronorm should be continued as normal, for the same reason.
Since we hear from so many members who find that their bodies do not adequately convert T4 to T3, and continue to have hypothyroid symptoms when taking T4 med only, I also wanted to ask if you have been tested for Free T4 and Free T3, the biologically active thyroid hormones. If so, would you please post those results and reference ranges shown on the lab report? What symptoms, if any, do you have? If tested for Vitamin D, B12 and ferritin, plese post those also.