If it has been rejected then you can simply make the corrections required to fix the rejection AND at the same time add the new information, and re-submit your CORRECTED e-filed return.
If it has been accepted you will have to prepare and mail an amended return ---BUT WAIT until you receive your refund before filing the amended return.
A Form 1040-X amended return MUST be PRINTED and MAILED; and usually takes 3-4 months to be processed. Form 1040-X is usually not available until mid-February.
Perhaps some terminology/definitions would be in order:
AMEND:- your return is what you do AFTER your return has been filed and accepted by the IRS and/or state. (No additional charge)
CHANGE:- your return is what you do BEFORE your return has been filed --simply go back to the respective information and change it as needed.
CORRECT:- your return is what you do AFTER you attempted to file your return and it is rejected by either IRS, or state --again, simply go back to the respective information and change it as needed.
Above all DO NOT DO ANYTHING until you find out if your return is rejected or accepted.
NOTE: When mailing a printed return it is always a good idea to go to the Post Office and mail it 'Certified' with 'Return Receipt'. That way you will have proof that they received it and when it was received
