I'm sort of agreeing with
@Totto regarding your classification; T2 v T1 v T1.5 v LADA (all variations on a theme).
That you have cut down carbs but still have scores as you do could mean either you've not cut as much as you thought, or whilst you have cut carbs, your body is not able to get the insulin where it's needed to lower those scores.
I think you need a three pronged approach:
Firstly, really have long long hard look at your diet. If you are off sick today, you should have time to do it, then act upon what you learn.
Secondly, make arrangements to speak to HR and find out what their feelings are on your job. Your line manager may be speaking without real reference to HR. HR are there to look after you as well as the company. Make sure the person you deal with in HR has some experience of dealing with diabetic/diabetes related problems. But, I know from past observation that probationary periods can be precarious things. Were targets set for your probationary period? If so, how are you against those? Do you know the Company's overall view on sickness, and what would lead to an HR intervention, based on absence? If you don't, you have to find that out really.
Thirdly, book to see your doctor again, and ask him if he will support you with your work issues. you may need some for of certificate from him, to appease the agency that you have recently been diagnosed with something likely to impact on your performance, over the shorter term. Obviously, agencies are commercial organisations, and what you describe is (as we know), how they make their money. In my time in line management, I never, ever used agencies as I just hated the prospect of gambling 20-30% of someone's on-track earnings, based on a couple of weeks performance.
Good luck with it all. You have some work to do, but in this game of diabetes, we hold many of the tools to improve our situation in our own hands. Obviously, that's not necessarily everything we need, but there's much we can do.