My son is a rising senior at VA Tech. Are you in the state of Virginia? The income you describe with your family size would usually put you as “estimated family contribution: zero.” The state of VA would grant you $5500 for tuition and the federal PELL grant would be about $5500. That pretty much leaves you needing to pay for room and board. You can borrow up to $5500 a year as a freshman. Virginia Tech does have a wonderful scholarship they award to zero EFC students. I believe about 50 students per year get the Presidential Scholarship Initiative. It would pick up the cost of room and board leaving you to pay for books and personal expenses. I think they mainly give it to first generation college students. You do not apply for the scholarship; you do the FAFSA and they select from that. I know someone who receives it and you have a similar GPA and SAT. They have some kind of support program that goes with it to help navigate registering for classes. I did not go to VA Tech but I love that place. A lot of departmental scholarships kick in after freshman year. My son got a generous award he did not apply for.
Even though you are receiving your AA you apply as a freshman. If you are going into engineering I believe you will have to retake some of your math. You can research that better on their site. Somewhere on their site there is a list of classes that transfer. Plenty of your credits will transfer.
If you don’t live in VA, focus on colleges in your own state. Most states have financial aid that favors state residents. VA Tech gives very little aid to out of state students. The people here can help you find other schools that give good aid. Good luck. https://studentsuccess.vt.edu/Academic_Excellence/psi.html