You are unlikely for a full ride anywhere and you’re not getting near an Ivy, even with a 1600 - abd Ivy isn’t necessarily your best engineering anyway.
Do you have demonstrated need?
Many schools meet need but don’t necessarily have engineering. And any school that meets need will be a tough admit, engineering or otherwise.
But have your family run the net price calculator for a school like U Miami. U Rochester just to measure your need because if a school says yiu can pay $50k, then they won’t give you need to $5k.
Your bigger issue with your stats is going to e getting into an affordable school.
A western Carolina is ABET and you can get into the 20s. A Southern Illinois is similar.
You can look at Berea College which charges no tuition. Their program isn’t exact to what you want though. Of course they have a Bio Major and health major too.
There are easier schools to get into but affordability is your issue. Also you cannot take loans - only up to $5500. Your parents could but why be strangled by loans?
Perhaps the military (rotc) or community college if you can find a low cost one makes more sense.