Toyota has been building Corollas for many years. They are not all the same. It would help if you told us the age of your Corolla.
It’s hard to imagine how a tire problem could affect the hood latch.
“Latch half broken?” No, sorry, it’s either broken or it’s not. There is no “half broken.”
But if the hood won’t close properly there is a problem.
I suggest you lubricate the hood latch. I’ll bet it will work a lot better with a little lubrication.
I once had a Toyota Corolla’s hood fly up at highway speed. Very scary, but no crash. But that was 35 years ago. I doubt your Corolla is that old (you didn’t tell us your car’s age).
Modern cars have a secondary device to prevent this from happening.
Please give us more information about the tire blowout, and how it affects the hood latch.
You’re hood won’t fly off, but it might open if the latch isn’t working, and you don’t want that to happen.