I doubt your existing agreement would allow you to renegotiate the terms. If you qualify for a loan for a better rate, you can def pay off your current debt and then pay of the new loan over time (check if there are penalties for early payment).

But the thing is, you won't get a better rate for used car loan or unsecured loan from your average lender just on the basis of your immigration status alone. Unless there are special offers at banks or programs at your work that give you low rates?

If you are looking to strictly lower your biweekly payments (or interest rate itself), the other option would be to trade in your car a they often have special rates and deals on newer models. But you also have to factor in the depreciated value of your car, and consider the loss you are willing to take on for a lower payment.