Don't worry, all of your reactions are perfectly normal! We have all been there in the beginning, believe me
The thing about cats is, they can tolerate much higher BG values for much longer than, say, humans. It's not at all uncommon, especially for newly-diagnosed cats, to see numbers in the 400's, 500's, even higher. I don't even want to think what that would feel like for a human

, but with cats, most of the time the damage only comes with numbers like that over long periods.
Normal BG range is roughly 50-120, so the numbers up in the 200's you've seen are definitely diabetic. On the higher end there, they're likely over the renal threshold (varies among cats), where the glucose spills over into the urine, but, again, that's really more of a concern over the long term.
In general we're much more concerned on the lower end. Unlike high numbers, low numbers can be
instantly dangerous, even fatal. So the recommendations and advice about shooting are conservative on that end. The 200 cutoff for shooting isn't because the numbers over 200 are dangerous and need insulin, it's because it may not be safe to shoot numbers
under 200. As Janet said up above, after you get some data and see how Nala reacts to insulin, you can start to relax that rule and shoot lower numbers, we just don't like to see it done in the very beginning while you're still getting used to everything.
I'm sorry we don't always explain all these things in detail. There's just soooooo much to learn in the beginning, I maybe err on the side of being too brief because I don't want to bury new people in the details, but sometimes that makes things even more mysterious

.
Anyway, back to Nala! Even though she climbed back up for a bit, she's spending an awful lot of time in blue numbers for a cat who has skipped several shots

!!! She really is looking very good, I'd say

.