First: Go to Ranch designs and get some replacement wheels (W/ tires) for the cars you already have! Then . .
Two: Go to Super-Target and buy the SCX Compact cars they should have several to choose from. If you are far from a Super Target, try Ranch designs they sell SCX cars as well and you can combine your order with the replacement wheels!!
Three: Yes the Carrera cars will run, but I believe your set is an Artin clone and is probably rated for 6 volts, the Carrera and SCX cars will run fine on it, but they are rated for 12+Volts and might be a little slow @6. If your house is like mine you probably have a 8,9 or 12volt transformer left from some other source that can be pressed into service as a new power supply for the new cars for no additional money!!