So $100K in debt is not worth it - and you can only borrow $27K, so that puts an end to that anyway. Your parents can borrow but you can’t.
$100K in debt (means you need to borrow more due to up front fees), over 10 years - depending on rate but assuming 8.1% (and 100K doesn’t net you 100K) is $1110 a month - so how will you pay that?
Don’t forget, colleges have inflation too - tuition, room and board. Costs if you move off campus.
The question to ask your folks is - if they’ve saved $100K - can they contribute anything each year in addition, out of their normal earnings. It may not e the entirety of the difference but maybe they have another $5K or $10K or $20K.
You really need to have the chat with them - given the monetary situation.
I know a young man at UTK in CS - and he had a great internship last summer and another at a leading place later this summer.
I don’t think anyone, myself included, will tell you reputationally or even opportunity wise a UTK can measure up (although in the end, one only can get one job or go to one grad school and in this case the school will matter less).
But one also can’t stay at the Ritz Carlton if all they can afford is the Fairfield Marriott - and even if your parents borrowed $100K on your behalf, how will they pay back the $1110 a month (for ten years). I assume they have a mortgage, car payment, and just life - and it sounds like they’re already stretched.
So in the case that you described, if the finances are as you described, you have to remove Ga Tech from your consideration set. But talk to your folks - if you really want to go to Ga Tech, maybe they have the ability to contribute yearly too - and you can assist with a summer job and eventually internships, etc. And maybe a part time job at school - although with CS that can be tough - and you can’t count on those for more than a few thousand a year.
And you can do very well, just as well, coming out of UTK - in aggregate less likely, but aggregates are just that and you’re an individual - so bust tail, apply for lots of internships after 2nd year, and be glad you won’t have debt strangling you or your folks!! And that gives you a lot more flexibility in life to do the things you want and when you want.
Best of luck.