Sure it is okay to use your own car for a road trip. But you have to weigh risks. Not many people have a lot of extra money lying around, just incase their car breaks. You are looking at tires, which aren't cheap, many people forget about those, and all the wear and tear on the rest of the vehicle. On the other hand, the rental car, costs money to. You have to pay for the gas, some like you to get insurance, whatever they charge for the day and if you go over your mileage. Plus you need to take pictures of the rental car before you take it, do a complete investigation, cause if they find something when you get back, that WAS there when you took it, they can charge you.
You can have a brand new vehicle, and something can go wrong. There is no way to tell if many parts on a vehicle will go. Some give you signs, and some don't. It is all a gamble.
Are you planning this trip alone? If you have others going, do any of them have a credit card, and you could all share the bill? Or look into bus trips.
There are many bus trips that run to other states, and all you have to do is buy the ticket