Is it worth to fight for? or just movee on ?

ive been with this guy for 2 years i love him to death! during feb-begining of march we went on a break because our fighting was getting to much. We broke up for 3 weeks but during it i hu with this random kid cuz my friend took me out one night and we were drinking etc.never told my bf,just wanted to forget about it. Last week he broke up with me because he "heard" i cheated on him. Obviously i denied but he still didnt take me back...I admitted it to him today but I dont want to lose him but he tells people were done for good... Was it considered cheating and is it really over? Or is he just being stubborn in response to hu with the guy and i should leave him alone for a couple weeks?