If the work study went to you, and not to pay for education, do not include that amount.
According to the IRS:
"Veterans' Benefits
Payments you receive for education, training, or subsistence under any law administered by the Department of
Veterans Affairs (VA) are tax free. Don't include these
payments as income on your federal tax return.
If you qualify for one or more of the education tax benefits discussed in chapters 2 through 12, you may have to
reduce the amount of education expenses qualifying for a
specific tax benefit by part or all of your VA payments.
This applies only to the part of your VA payments that is
required to be used for education expenses.
You may want to visit the Veterans Administration website at
www.gibill.va.gov
for specific information about the
various VA benefits for education.
Example. You have returned to college and are receiving two education benefits under the latest GI Bill: (1)
a $1,534 monthly basic housing allowance (BHA) that is
directly deposited to your checking account, and (2)
$3,840 paid directly to your college for tuition. Neither of
these benefits is taxable and you don't report them on your tax return. You also want to claim an American opportunity credit on your return. Your total tuition charges
are $5,000. To figure the amount of credit, you must first
subtract the $3,840 from your qualified education expenses because this payment under the GI Bill was required
to be used for education expenses. You don't subtract
any amount of the BHA because it was paid to you and its
use wasn't restricted."
https://www.irs.gov/pub/irs-pdf/p970.pdf
