Some simple facts about lipo's:
1) The C rating is a way to calculate the continuous current that the battery is able to supply, when/if asked by an esc. C rating x Capacity = Continous current draw available.
2) You could put pretty much ANY C rated battery in your car with ANY esc (with a lipo/low voltage cutoff) and it would be fine if used properly!
With lower C rated battery your car is just slower, and won't run for as long. The C rating of the battery indicates the limit to it's current delivery to the ESC when asked. Even a 10C battery would be totally fine with the highest power rated ESC known to man...it'd just be slower, and won't last very long!
3) Lipo's only puff up when they are damaged. There are many possible reasons for this. A few suggestions might be: because it's been over discharged, over charged, charged incorrectly, old and worn out, connected up to your esc incorrectly, shorted out or has a manufacturing defect of some sort.
The original post asked if the car was just too powerful? Simple answer...NO!
The battery is the power source! Your car is only as powerful as the battery. Your ESC and motor can only use as much power as your battery lets them have, they will just handle it better the higher rated they are.
But...if your batteries are too big for your ESC and motor, you could damage your esc and motor! And if your battery is too high powered for you to drive, you'll damage your car!!!

But since all the racing ESC's/motors/lipo's are designed to work with each other, as long as you use them right they'll be fine...it's not as dark an art as it might appear!
Hope it helps