If you need money, it comes from either:
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Schools giving to you - merit or need aid.
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Lower tuition to begin with
With a 3.8 at a private HS, you may be fine or may have no chance.
I’d suggest you speak to your counselors - they’ll know where students like you have attended in the past.
If you want to go to med school, the where will matter less - but yes, you do need the 8 year budget.
You can go to some schools for near tuition free with those stats based on automerit. There’s many schools, even similar in size to those you seek, that will give you money
Here’s one example (of a small program within a large school that would cost you maybe $20K a year - all in. Princeton is near four times that. Will they have a higher percentage get into med school? Yep - but is it because they are Princeton? I don’t necessarily think so. I think it’s because they had top kids to begin with - and those kids would likely be successful no matter where they are.
Best of luck to you.
But first step is get with your counselors - and develop a realistic plan based on your accomplishments, academically and otherwise (including budget).
McCollough Scholars – Pre-Medical Studies at the University of Alabama (ua.edu)