I'm so happy that I finally got my coworker fired
That's not something to be happy about. Did it feel good to have someone fired?
A little bit, I was just tired of listening to his complains
The behavior is completely unacceptable. Just because you are tired of someone, doesn't give you the right to have him fired.
I'm tired of hearing people's complaints and I just couldn't ignore him anymore
Did you try talking to him about it first? He might not of been aware that he was even bothering you. It's good to try and talk through things with a coworker before involving the boss.