I have already filed and been rejected multiple times. Can I still file somewhere else or do I have to file through TurboTax and mail my returns in?

You can go somewhere else since your return was rejected, but you already paid for the Deluxe version. You can also state why your return was rejected & maybe someone can help you.

If you paid, you don't want to go somewhere else and pay again.

Unless you fix the reason for rejection, your return will also be rejected from other tax filing sites. It is being rejected by the IRS and not by TurboTax.