I've worked in Care before - it's hard work! Depending on whom you're caring for, there may not be much of a routine so you might find your blood sugar can vary. Test lots and eat something extra if it looks too low. It doesn't have to be at hypo level for you to top up with a little extra carbs. That should help keep you going if there's a delay to your break.
If something was agreed - you having first lunch - and then that was changed, I think you need to speak to your manager and find out what's happening. I get that you've not had a good experience in your job even before being diagnosed with diabetes, but don't let yourself be bullied out of a job.
On a separate note - are you counting carbs and adjusting your insulin to match what you're about to eat? If not, then that's something you could ask about.
Did you have a GAD test to confirm you're not Type 1?