Kid ruining my reputation?

There is this kid at my school. Me and him were never really friends. He is like the kid you only talk to in a cl where you know no one else. Well the other day in this music cl there was a sub. The kid was talking crap to this freshman so they decided to fight. The kid got his whooped and i literally had to pull the freshman off of him. Afterward he kept talking about it and i told him to just be quiet you win some you lose some. He started saying how he could beat me up. I fought him but not really. I punched him a few times and then just held him down. I got behind him so i could have easily messed him up but i didn't i just proved that i won then left him alone. So yesterday i guess his face was swollen because of how bad the freshman punched him up. He told everyone his face was swollen because i threw him down the steps. And punched him in the head. Didn't do anything to this kid. I know for a fact that i never through him down any steps and he is completely making that up. He still continues to try to follow me around and go where i am going. Asking me to pay for him after he follows my friends around at lunchtime. Then going and saying that i am lying and threw him down steps. I am thinking about actually throwing him down some steps now. What should i do?