I already filed and submitted my taxes and did not claim myself. My mom was unable to claim me on hers because I made over $4200 in 2019. Does this mean my taxes were done wrong and need to be amended

Income is just one of the tests if you can be claimed.  She might still be able to claim you.  How old are you?  Are you a full time student?  Who can I claim as a dependent?

https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/26781

If you need to claim yourself you can amend.  How to amend an Online return

https://ttlc.intuit.com/community/amending/help/how-do-i-amend-my-turbotax-online-return/00/27577

If you already completed your taxes and filed then your mom cannot claim you. Also, if you filed then you claimed yourself...you do not enter yourself as a dependent if you are filing on your own.