If you have not yet been notified if your return was accepted or rejected you will need to wait to see if your taxes have been accepted or rejected.  

If rejected, you will simply need to fix whatever error caused it to be rejected, then remove your son in the My Info section and then resubmit your return.

If accepted, once your return is processed you will need to follow these instructions to Amend Your Return once the 1040X is available in Turbo Tax. You will see your refund/amount due set back to $0, you will then remove your son in the personal information section. 

Your amended return must be paper filed.  When you get to the end, it may "appear" that you can e-file it, but it must be mailed.  It will take 10-14 weeks for the IRS to process your amended return.  Once submitted you can check the status of your amended return here Where's My Amended Return

If your return was accepted and you file an amended return, your girlfriend will need to print and mail her return IF she wants to claim your son or it will be rejected by the IRS for duplicate dependent SSN.

Your GF does need to wait until your amended return is processed. She can file now and claim the child. But, she can no longer e-file. She will have to mail in a paper return. Her return will be processed in 6-8 weekks

 If you and the other parent live together, either one of you (but not both) may claim the child. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.

If you and the other parent live together, only one of you can claim the child for any tax benefit. The interview is confusing (it's designed for divorced parents). The second parent should not enter the child, at all.