If your son cannot be claimed as anyone else's dependent and his SSN has been put into the system---by your tax return---he will need to file his own return by mail. Waiting for your amended return to be processed will not help him. He cannot e-file this year. He will need to print, sign and date his return in ink, and mail it in.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as certified mail so you will know the IRS/state received the return.
Federal and state returns must be in separate envelopes and they are mailed to different addresses. Read the mailing instructions that print with your tax return carefully so you mail them to the right addresses.