Thyroid hormone is responsible for the 'turnover' or metabolism of protein, carbs and fat.
If you are hypothyroid, you tend to have low energy and to store excess energy as fat, rather than burning it off.
This would suggest either low BG levels, or an inability to process carbs within the muscles themselves.
Either way, assuming that your thyroid levels have been normalised through administration of exogenous thyroid hormone (thyroxine) then there should be little conflict or interaction between the two conditions.
However, I did say "assuming". Basically, you need regular bloodwork done to accurately asses your T4 and T3 (thyroid hormones) level in the blood. Without this insight, it becomes a guessing game to a certain extent.
Here is an article which seems to state that blood glucose is unaffected by hypothyroid. It's a long, dry read though :?
Here is the most relevant paragraph for you:
"Typically, blood glucose levels are unaffected by hypothyroidism because insulin sensitivity is not altered. In fact, in patients utilizing exogenous insulin, there may be a decrease in insulin requirements from reduced insulin degradation.8 Therefore, typically, glucose remains stable or improves while a person is hypothyroid. Once thyroid treatment is initiated, patient education and close observation is vital because normalization of the thyroid may potentially lead to higher blood glucose levels and loss of diabetes control"
All the best,
Alex