How to verify a proof prior to peer review in mathematics
Ask your teachers. They know you well, probably know math better than you, and are your closest connection to the academic world. That means they're the most likely to be willing to look through your proof, capable of finding an error you didn't spot, and if they can't find anything wrong, they'll know who to approach next (e.g. their professors from when they did their degrees).

You could conceivably approach math professors at your local university directly, but you risk coming across as a crank and being ignored. If you're able to get your math teacher to vouch for your proof, that would lend strength to your claim.