I am a resident of NY state and worked in Georgia for three months, my employer did not
Withhold state taxes for Georgia. All state taxes was for NY state? Is this correct? If no how do I correct it when I file my income tax?

If your Georgia income is more than Georgia filing requirement, file Georgia tax return. If you owe taxes, pay it with your tax return.
On NY tax return, you will report worldwide income including Georgia income. Claim credit for taxes paid to Georgia. Your U.S. Tax Return: Working or Living in Two or More states