There are colleges that do provide need based or merit aid that will cover tuition, and then room and board costs. These awards are not all that plentiful.
Do you have significant financial need…and the stats to get accepted to a school that guarantees to meet full need for all.
Do you have significantly high stats that you would qualify for merit aid?
If you get financial aid that exceeds tuition, fees, books…it will be considered taxable income for the student.
Ok…I found your stats…
And you are in NY state and say your parents can pay $20,000.
I would suggest that you apply to University of Alabama right now…and complete the scholarship application as well. I believe you will get sufficient aid that your parent contribution of $20,000 will cover any remaining costs.