Yes, you should file by mail, your e-filing as independent will be rejected by the IRS because your dad already filed his taxes and claimed you as a dependent. You can do it before or after your dad amends his return, and he's right, it's better to wait until his original return will be proceed by the IRS and after that file an amended return. Your options - wait until your dad amend his return and add his Form 1040X to your return, or file now and add a note to explain what happened. Expect a delay in the processing time in any case.
