Fight? Good or bad????

Ok let me rephrase this.I didn't want this kid to sit next to me and I repeatedly told him to plz move and I was joking most the time but he's an *** whole and thinks he's funny and I'm really sick of him (no excuse) (this was in spanish, I'm 13) so I finally pushed him (lightly trust me) and me tripped over himself and fell farther then he should have. I felt bad after. Anyway He got up and was pissed off so much, he was smiling when he punched at me and missed. He tried again and I grabbed his and and he swong with the right hand and I grabbed that one to and wrapped his arms around himself (people were crowding to see what'd I do) and held him still and yelled repetitively at him to "comb down!" and he kept jerking so I grabbed his arm (right) and put him in a full blown chicken wing and yelled at him "comb down! And I'll let you go!" and he did. So I let him go and sat down and he seem ok, so I thought everything was ok. Later I got sent to the principles and was "introuble for starting a fight" which I think is like 10% my fault. Anyway I was wondering if I did the right thing?