Basing your team around Spirit of Competition and Flamethrower, I would definitely recommend picking up some new pets. One would be Fel Flame (or something similar that has Conflagrate) - the nice thing with that particular pet is it's fairly high level so it won't take long to level it up. Corefire Imp might be okay as well depending on what abilities you choose, though Fiendish Imp would be better. Similar abilities but it also has Nether Gate if you want to force swap your opponent's pets, which is always annoying.
You might just have to try mixing and matching a few pets to see what works for you. Don't get discouraged if it seems hard at first (I had something like a 95% loss rate at the start haha) because everyone has to start from somewhere. Watch what your opponents do to pick up tips and tricks to improve your team.