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You may not be eligible for an additional stimulus payment for your newborn. The third round stimulus payment you received was an advanced payment on the Recovery Rebate Credit on your 2021 return.  However, since 2021 tax returns had not been filed yet the IRS used 2020 tax return information.  Therefore you received payment for three people on your 2021 return already; that the third person is a different person is not a factor.

Having said that, if your 18-year-old son still met the criteria in 2021 to be a dependent he could have still been on your return and filed his return as well.  He would need to indicate on his return that he "Can be claimed as a dependent on someone else's return."  

To be a dependent he needs to meet all the tests in one of the two categories below.  If he fails any test in both categories he cannot be a dependent.

To be a qualifying child: 

• The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.

• The child must be (a) under age 19 at the end of the year and younger than you (or your spouse if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse if filing jointly), or (c) any age if permanently and totally disabled.

• The child must have lived with you for more than half of the year.

• The child must not have provided more than half of his or her own support for the year.

• The child must not be filing a joint return for the year (unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid).

To be a qualifying relative:

• The person can't be your qualifying child or the qualifying child of any other taxpayer.

• The person either (a) must be related to you in one of the ways listed under Relatives who don't have to live with you , or (b) must live with you all year as a member of your household (and your relationship must not violate local law).

• The person's gross income for the year must be less than $4,300.

• You must provide more than half of the person's total support for the year.

Publication 501