I need to add my spouse's social security number. Do I need to make an amendment to my tax returns. Will this affect my stimulus check?

Did you file as SINGLE?  Was it accepted?  If you were still married on Dec 31, 2019 you need to file a Joint return or as Married Filing Separately to add your spouse.  So how did you file without the ssn?  If your return rejected because the ssn was missing you do not amend.  Just fix it and resend it.