Is it normal that i can not get over my first love?

I have broken up with my first love for 4 months. Our relationship had last for 3 years and suddendly he said that he wanted to break up with me at my very birthday. It was so painful, despressed, crazy and heartbreaking. Eventhough he said that he will never abandon me, he will be there when i need him. But he got a new girlfriend now, exactly 4 months after our breaking up, but He still keeps in touch with me. Everyday was hell, i could not breath, eat nor sleep. Memories about him make me hurt so much. Even worse, I saw him and the new girl together, holding hand, kissing and be all lovely dovely right before my eyes. My life is upside down right now. I keep on telling myself that I should not contact him, not calling, not texing anymore and in the end I just can not stop my self. There were times when I called him and we were handed out together like the old times, do stuffs that you can call it cheating. At that time, when I was with him I didn't feel lonely anymore, but when the fun was end, we once again went seperate ways. He said he still cares for me, but i guess he only cares for me when he gets to see me!?I don't know what is right or wrong anymore...