Wow. That really sucks! I am so sorry. But I am glad you are being treated. Tick diseases are some of the most frightening, I think..
I had a rash associated with a tick bite about a year ago- we do not have Lyme's disease in Eastern TN- but we have a similar disease known as Southern Tick Associated Rash Illness (STARI). The doc had not heard of STARI, but actually took notes so he could find out more about it later as he had seen several cases resembling Lyme, but the individuals hadn't been outside of the area..
ANYWAY... sorry for the ramble. He finally gave me doxycycline, and the rash started clearing up within a few days. Did they put you on doxycycline?
I was not a T1 diabetic then (that I know of!).. so I can't answer the sugar question. But I had a lot of nausea and dizziness while on the medication, and a few episodes of tunnel vision. It's such a nasty drug, imo.
There were a few things that popped up when I googled doxycycline and diabetes... but I'm sure you've probably researched it already!