Would my mortgage or car loan change?

No. Your mortgage and your car loan keep running on exactly the terms you signed. The rate does not reset, the balance does not jump, and the monthly payment does not change. A loan is a private contract, independence does not rewrite private contracts, and keeping the dollar in circulation means there is not even a currency question to worry about.

A loan is a contract, and the terms travel with it

Your mortgage and your auto loan are binding private agreements: a principal balance, an interest rate, a payment schedule, and a payoff date, all spelled out and signed. A change in which government Texas answers to does not reach inside that contract and alter its terms. This is the same settled principle of international law that protects your property: lawful private contracts survive a change of sovereignty and remain, as a matter of principle, unaffected. Your rate is the rate on your note. Your balance is the balance on your note. Your payment is what you agreed to pay. None of it moves because Texas governs itself.

Keeping the dollar keeps your payment identical

Here is the practical key, and it is the most important sentence in this answer. Your loan is written in dollars, and an independent Texas can keep the dollar in circulation through the transition and for as long as it serves Texans. Several sovereign nations use the U.S. dollar as their everyday money with no trouble at all. As long as the dollar stays in use, there is no conversion on your loan, no redenomination, and no exchange-rate question. A dollar-denominated mortgage stays a dollar-denominated mortgage. The number you pay each month is the same number it is today.

Who you pay can change hands without your terms changing

Loans get bought, sold, and transferred between servicers constantly under the current system, and your terms never change when they do. Millions of mortgages change servicers every year, and the only thing the borrower notices is a new address to send the payment to. If your loan happens to be held or backed by a federal entity today, the servicing could move to a Texas institution as part of the transition, and you would simply mail the check, or click the button, somewhere new. The rate and the balance ride along untouched. That is a routine administrative handoff, not a change to your deal.

Texas has the lenders and the depth to carry it

An independent Texas is not short of institutions to hold and service loans. Texas has more than 200 state-chartered banks, a mature regulator in the Texas Department of Banking, the deep credit-union and mortgage-lending industry that already operates here, and the world's eighth-largest economy underneath all of it. The capacity to originate and service mortgages and car loans is already Texan and already at scale. Lending does not seize up for lack of institutions, because the institutions are here and already doing the work every day.

Sound money is the long-run friend of your budget

Over the life of a loan, the biggest variable in a household budget is the value of the money itself, and the inflation that erodes that value is made in Washington. The dollar has lost a large share of its purchasing power over the decades, which quietly raises the real cost of everything around a fixed payment. An independent Texas leaning toward sound money, with no personal income tax, is steering away from the force that makes a budget harder to balance over time. Independence does not threaten your loan. It points toward steadier ground under the budget that services it.

The bottom line

Your mortgage and car loan continue on the same terms, because they are private contracts and independence does not rewrite contracts. Keep the dollar through the transition and there is no conversion to think about. The most you might notice is sending your payment to a Texas institution instead of a federal one. Same rate, same balance, same payment.