You report the child care grant money as income as the University stated. You must report the full amount that is shown on the tax forms that they send you.
Because the grant is taxable to you, yes you can use it to claim the Child and Dependent Care Credit. However, another requirement to claim the Child and Dependent Care Credit is that either you or your spouse will need earned income. This credit allows for one of you to be exempt from the earned income requirement if you are a full time student but not both of you.
To see more information about the Child and Dependent Care Credit:
https://ttlc.intuit.com/replies/3301418
