I was in a car wreck. My car was totaled, how do I know if the insurance company is giving me the right amout for my car?

Did u dispute the estimate from the insurance company? Usually they give an average value on what a vehicle cost by running through special lists that they have regarding depreciation values of your car, with your approximate miles, with your car's approximate age.  Did u give them back the car or did they cut you a check and u can go repair it someplace?  You can always ask the insurance company of a detailed accounting of how they arrived at the value of your car.  You're, of course, never going to get retail value, which is what you'd find being sold online or in a paper. 

Auto Trader isn't a reliable source for the value of a car, it's just a collection of advertisements.  Most insurance settlements get used car values from one of the published guides.  It's based on the year, make and mileage, with some consideration for optional equipment.  But the brand new tires don't change anything for this purpose.

The companies that publish the used car price guides have websites, where you can enter the information about your car and get the three estimated values.  Going from the highest to the lowest, these are retail (what you'd expect to pay to buy the car from a dealer), private sale (not to or from a dealer) and trade-in (what you'd expect to get toward the price of a new car, for your old one).  The insurance value is more likely to be the trade-in value.

If they sent you a check for the $7547, you will probably have to chose between taking the money (depositing the check) or waiting to get paid and fighting them.  Read the check, and anything that came with it, very carefully!

And if you want to fight them, having a lawyer write the nasty letter for you might be worth the cost.  You can find help at http://attorneypages.com