Not that you should appreciate people like that
You need a new boyfriend I think.
Maybe he just wants to stay home and do his own thing for a while? Does it matter if he is busy doing something important or not? He said he didn't want to hang out today....so, I don't get the anxiety. It's not like he broke up with you. As long as he isn't playing around with someone else, I don't see why he can't have some space.
If you haven't talked in days, then it sounds like he trying to give you the brush off. Some guys will do that when they want to break something off, but they lack the integrity to just be up front about it. That might not be the case, but now that you mention it's been DAYS, then it's a distinct possibility.
Honestly, I think you had better brace yourself. He should not be shutting you out. Wanting some time to himself is fine and dandy...but if he is distancing himself and can't at least tell you why, then I'd be careful of my heart.