Do you not have any eligibility left for government student loans? Even if you turn 24 you should still be eligible and if your parents can’t get Plus loans you should get an extra $5000 in student loans.
If you want a private STUDENT loan, then there are several lenders like SallieMae, Discover, SoFi. The amount will be tied to your total cost of attendance which does include living expenses.
Your sister can take out any loan she wants. If it isn’t a student loan, she’ll pay the interest rate the bank sets for an unsecured loan (usually pretty high). This doesn’t seem like a good plan. If she borrows extra on her student loan and gives it to you, that’s her choice (but not very nice of you).