Is this normal or no?

so I was dating this guy for a while and he was always so swag and would make me feel better if I was having a tough time. We always had fun together and he'd always talk about the different things he's like to do with me. A couple weeks ago he broke up with me and I was devastated. The thing that made me feel so bad though was he didn't give me a reason why. At first we would still message eachother and he was still nice he'd say hi to me in the hallways and even smile. But now he doesn't answer my messages and when he sees me in the hall he looks down or away from me. I realize he doesn't want to be with me anymore but I don't want him to be my enemy. I also follow his twitter and I saw him posting about how sad he was so I sent him a message asking if I could help and he didn't reply but a little while later he was flirting with some other girl online. Am I being too clingy to him? Cause I feel like I am. Or is it normal for exs to want to be friends after they have broken up, and even be a little jealous when their ex is with someone else. I feel like an awful person.
Is this normal or no?
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