I am filing my taxes for the first time and received a rejection code IND-516-01. My parents are claiming me. Do I still need to file taxes for myself?

It depends, please see the filing requirements for dependents below:

 https://ttlc.intuit.com/replies/3302185

If you need to file you will have to mark that you can be claimed as a dependent:

1. Click "My Info" from the left side of your screen
   
2. Click “Edit” next to your name
3. Please scroll down to “3. A few other things we need to know”  and answer "yes" under “Someone else can claim me as a dependent on their tax return”

Please see this FAQ on how to fix a rejected return:

https://ttlc.intuit.com/replies/3302275