Dr probably prescribed it based on elevated TSH (Thyroid Stimulating Hormone) levels.
Unfortunately getting levels quite right on that can take a little while since there is a bit of a lag in the body responding.
Chances are that your Dr settled on the 50 microgram dose based on your weight and TSH levels and you will then be called back in for more blood work in 3 to 6 months while they titrate up or down to what you need. Example of the calcs here:
http://www.globalrph.com/thyroid_calc.htm
Since being diagnosed T1 my thyroxine dosage has varied by around 125mcg and I didn't see much in the way of changes though I did increase my testing rate.
While you may not be obviously symptomatic for under active thyroid the TSH is kind of a definitive answer really and your body may be compensating to some degree such that you aren't noticing the symptoms.
Best advice I can give you is to just up your testing for a few weeks to see what impact it has on your BG and insulin requirements (if any) and speak to your Dr and get your blood test results to get a better understanding of his/her reasons fro the decision to start you on thyroxine.
From my own experience and research I have seen no adverse interactions of any diabetes medication with Levo Thyroxine, though if you are on simvastatin then I would suggest that you talk to your Dr about switching since there are known and documented details about simvastatin causing problems with levothyroxine, mainly inhibiting the thyroxines effectiveness. Since I was on the max dose of thyroxine when they started me on statins I insisted on atorvastatin and my GP actually agreed with me on that score.
If you still aren't sure or you want to make sure it is not likely to cause issues with anything else you may be taking then you are probably best to talk to your pharmacist to start with since they tend to have more of a clue about drug interactions than Dr's in my experience.
Otherwise nothing to worry about with thyroxine, you will have a bit more energy though which is nice
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