Q. When I fill my taxes will I owe?
A. No. You'll most likely get a "refund", even though no money was actually withheld due to generous refundable credits for child dependents and earned income.
Q. Should I amend my w4 and withhold a set amount myself?
A. No, unless you know, for a fact, that your employer is wrong. Even then, there is no penalty if you owe less than $1000.
Use this tool to see an estimate of your tax due or (more likely) the "refund" you will get.
https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1