I got my report card today and it said that I got held back. Is there anything I can do to not get held back or, in other words, get promoted?

I highly doubt that you could appeal that decision. They must think you have to repeat that grade because you didn't learn enough to pass the tests and move up. I've never heard of any school that has reversed that decision. Just work harder next school year to make up for it.

This is something that should have held your complete attention many months ago, not now.

See if summer school is an option ,

Usually it says that on your report card though