Whether or not you have to pay Federal Income Tax is determined by quite a few factors. TurboTax will apply all allowable Credits and Deductions based on the information that you have entered, therefore letting your know if you will owe taxes or not.
Since the child is your Grandson (blood relative); if he is under the age of 18 (or 24 if a student, you provide more than half of the child's support, and he lived with you for more than half of the year, you can claim him as your dependent. This will allow you a dependent exemption for the child. This exemption is a $4050.00 downward adjustment when determining your Taxable Income. Please keep in mind that this exemption does not always translate into a refund.
If the child has already been claimed on another Taxpayer's return, the IRS will reject your attempt to e-file. If the IRS rejects your return and you feel that you are absolutely entitled to claiming him as a dependent, since it is quite late in the Tax Season you must file your return by mail. If the person that claimed the child is willing to make and amendment to their return to remove the child in order for you to claim them, you must file and Extension to allow time for the amendment to be processed by the IRS, since it can take up to 16 weeks.
Below are FAQs with instructions on Printing your Return to file by Mail, and for filing and Extension:
https://ttlc.intuit.com/replies/3401713
https://ttlc.intuit.com/replies/3301811
