I concur with the moms that it seems like an extraordinarily bad idea to graduate with $100,000 in debt for an undergraduate degree. Even for a US citizen with no immigration worries, let alone for an international student.
But let’s think through the details of your proposal. It’s not easy to get a $100,000 loan from a private US bank. Does your relative own real estate in the US that they can take a mortgage out on for you? If not, are they a US citizen with a sufficiently high income that a bank might trust them to repay an unsecured $100,000 loan? (Google debt-to-income ratio.)
Lastly, I would like to caution you to factor future tuition increases into your budgeting. For example, annual tuition and fees were $40,741 in 2013-14 and $52,002 for 2017-18. That’s about a 6% annual increase. If that trend continues, tuition and fees might reach $67,000 in your 5th year.
If you are lucky, the income from your co-ops will pay for future tuition increases. You are still short about $100,000 even with the co-op income already accounted for.