Maeve,
You do sound like a LADA - high BGs when low carbing and exercising. And of course you're worried about high numbers. You're right to be. (Only a fool would not worry, actually.)
So, ask for a GAD antibody test. Make the point that your BGs are in the context of very low carb intake (put the figures in a table and take it with you - weekly averages carb intake and BGs if you have them). Normally, low carb would drop your BG levels to 6-ish. A GAD test will establish if you have antibodies to your own insulin, ie if you have autoimmune diabetes (which means Type 1, of which Type 1.5 is a subset).
Once you've got that result, if you are Type 1, you can start to take insulin and you will begin to feel SO MUCH BETTER, I can promise you.
In the meantime, to understand the subject and to follow his excellent approach, I recommend you buy *Dr Bernstein's Diabetes Solution*, available from Amazon on Kindle or as a paper book. He sets everything out, and it will gradually make sense.
By doing so, you'll be taking control of your life again. Which always feels sooooooo much better.
Lucy