How much can your parents pay? If they can pay $12,000 a year, apply to University of Alabama…NOW. It’s possible you will get a decent merit award. However, without knowing your CR/Math SAT scores, and your GPA, it is hard to give more precise information.
Need blind schools do not consider your ability to pay when they are reviewing your application for admission. This has NOTHING to do with financial aid.
Schools that guarantee to meet full need for all is probably what you mean.