Will the IRS let me file as an dependent on my taxes amend? The first time I filed I accidentally put that I can not be filed as an dependent. ?

Yes.  If you filed incorrectly and said you could not be claimed as someone else's dependent you can amend and change the way you answered the question about that in My Info.   You will not be able to amend until your first return has been fully processed.  And you have to wait for Form 1040X which will not be available until at least mid-March.

  If your mistake has caused someone else's e-file to be rejected (parents?)   they cannot e-file at all this year now.   The only way they can file is by mail, so they do not need to wait for you to amend.  They can mail their return any time.