Should I refinance my car or trade it in?

Okay so this is my current situation, I bought a car for my first time and I'm currently financing it with a bank ($350/month). I owe $12,500 right now but the interest is KIILLING me and I know my credit is really good right now because I'm being approved for ALOT of money. The other thing is that this car has too many miles, it's a 2012 Honda civic with 83,000 miles (Yes I know they messed me over bad but everyone makes rookie mistake). Should I trade it in for a new car or should I refinance this car and risk living with it? Even though I hear Honda are really reliable cars. What should I do?

We need more info. How much do you estimate the car is worth for trade and private sales. Go to kbb and edmunds, put in the miles to get the right value. And try to find the same car on CL to see prices.
What is your interest rate? How many payments do you have remaining?

Holy Cow, right 83,000 miles is a lot for a 2012. Most consumers do not properly calculate the discount that should be applied to car with above average miles. Example normal 2012 car has 36,000 miles, 83-36 = 47,000 miles over average, 47,000 x 10 cents per mile = $4,700 discount to adjust for the mileage.

Rookie mistakes do happen, and I'm guessing in simple terms you overpaid for the car. On that note, next time take this very simple effective advice. Take you time, shop around, go to a dealer with specifics like, "I'm looking to buy a three year old Accord, 4 cyl, less than 45,000 miles, etc. I have about 30 minutes to get some info, here is my contact info (hand it to them with name, number and car you looking for already written out), can you show me what you have in that range? " If they hem and haw, need to talk to manger, need to pull your credit, etc, at 30 minutes say thanks very much I told you I had a schedule. If you get the info I need please give me call. Drive to next dealer. If you want to go back, call manager and say I need another sales rep, Mr. A was a nice guy, but I'm on tight schedule and can't sit at the dealer for 3 hours. I'm ready to buy, but I can't consider buying from you if don't have the right information.

The the re-fi. Few lenders will re-fi a car. And you are most likely upside down so they would not do it.
If you can get a simple personal loan with installment payments and the rate is lower and the term the same, then OK, that might make sense.
Trade in, bad idea if you are upside down, just builds more debt and I'm sure your payments would be much higher.
I don't think it is the interest as just the total payment, which is interest and principle.
Most first time buyer have payment shock, as they think $350, no big deal. It is doing month after month after month that gets to you. And insurance costs go up.

Summary, make your payments and get the thing paid off. You made a mistake, just don't make a second one.
Sounds crazy, but try to pay extra, send in tax refund, sell some stuff you don't need, maybe a part time job.
Also keep good records on your payments, print all cancelled checks, and or keep all monthly statements.

The miles do not mean anything, Forget that. If the car is well maintained the miles are pretty meaningless.
You do not mention the interest rate you are paying or the interest rate of the new loan. Those would tell you if you will be in a better position financially. You can ask the bank what your Civic is worth as a trade in. (that might scare you into not trading) Do not ask the dealer what it is worth as a trade in because you will learn another lesson the hard way.(they will sell you the most expensive car for a premium price)
Best way out is to see it through and pay off the loan.

83,000 miles on a Honda Civic is very low mileage. Take care of that Civic and it will easily last 175 to 200,000 miles. The worse thing you can do is to make a bad situation worse by trading this car in on a new car. If you can't afford the current payment why would you think you can afford an even higher payment. Check around about refinancing the loan at a lower interest rate. Whatever you do keep driving what you now have and forget about trading cars. That would be foolish. If you simply can't afford this car then sell it and buy a much cheaper car. That would be a wise decision. In the future only buy what you can afford.

Your question can be answered very easily. Simply go to a couple or three of your local banks or credit unions and apply for a refinance loan. If they approve you, you can decide if their deal is worth accepting, and then go with the one that offers you the best deal. Done.