I feel annoying to my boyfriend, what should I do?

So, we've been dating for almost 8 months now. I've found out i'm super clingy- and I hate it. My boyfriend finds it cute whenever I'm with him, but he finds it annoying when I try to message him a lot when he's "busy". This has been making me feel awful lately...
Sometimes I feel like he's not really so much "busy", and more just annoyed with me.
I really don't want to be so attached, but I feel so dependent on him.I don't want to be like this, but I feel so hopeless. I would really appreciate some advice right now.