I mean this very kindly (as it's hard to show that in typing), but a "better position" and a "better school" doesn't always solve difficulties like this. Not to say that some schools aren't more difficult than others - they are - but all teaching jobs come with their level of difficulty. That being said, starting over could easily re-start your brain and help you feel better and more confident in your abilities. The bad thing would be when prospective employers ask you why you left your old job mid-year.
I'm sorry people aren't being as supportive as you need them to be. Teaching is tough and time-consuming, and a lot of people don't want to take the time to help newcomers because they're so overwhelmed themselves.
As others said above, this too shall pass. I wanted to quit SO MANY times (still do, sometimes when I have a bad day), and luckily my husband pushed me forward
Good luck, and I hope you find a better fit for your needs