Clingy?

I’ve been with my boyfriend for a few months now, and I still can’t get enough of him. I want to be with/talk to him all the time. He feels the same way. It’s not as if I don’t let him have his own life and own friends; I’m perfectly okay with him doing that. I’m also not the jealous type. I just always find myself wanting to be around him all the time.

Is this still considered clingy/obsessive? And could it cause problems later on? And how do I fix this? I get attached to people so easily, I hate it and I don’t want to ruin this relationship with my insecurities about him leaving me.