Can an increase in Leverthyroxine for the Thyroid increase your blood glucose readings

[The Bead Queen]

Hi I had got my blood glucose readings done to between 5.9 and 6.9 every morning by sticking to the Low Carb diet but my GP decided my Thyroid wasn't functioning properly so increased my dose of Leverthyroxine from 75mg to 100mg a day. Immediately my bloods went up to 8 and 8.4. I can't tolerate Dairy so I use Almond and Coconut milks and yogurts but the ones with the lowest sugar in them. Is it me or are these meds or my liver and pancreas. My Cholesterol levels were 5.7 and she wanted me to eat less fat as well as I've had a bad experience with Statins and refuse to take them.