My mother incorrectly claimed me as a dependent. When my return was rejected for this she amended her return, but mine still gets rejected when I try to file.

If you *can* be claimed as a dependent then that law does not allow you to claim yourself whether you are actually claimed or not. 

Amended returns take about 6 months to process but will NOT reset that your SSN has been used.

Nothing requires a parent to claim a dependent, but if they CAN claim the dependent then the person cannot claim them-self - tax law does not allow that. That is why there are two questions "CAN you be claimed by another tax payer?, and WERE you claimed?

Yes to the first means you cannot claim yourself, no to the second might allow you to claim certain educational credits that usually only the person claiming you could claim.

Also see:
https://ttlc.intuit.com/community/dependents/help/when-do-i-have-to-answer-yes-to-being-claimed-as-a-dependent/01/1994319

Sorry if she amended you will still have to mail your return.  Once a ssn has been used you can't efile it again even if she amends.  

How to mail a return from the Online version
https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/01/26258

Be sure to attach copies of your W2s and any 1099s that have withholding on them. You have to mail federal and state in separate envelopes because they go to different places. Get a tracking number from the post office when you mail them for proof of filing.