I'm sorry if this comes off sounding insensitive, I really just mean to be helpful. But honestly, if it's a new relationship and you are young...talking every day is overrated. It can also get tiresome -- especially if one person doesn't really have much to say since talking to you ten hours ago. Your lives aren't that complicated at this point -- so it's not like there is any rush to say everything there is to say.
Independence is attractive, and absence *does* make the heart grow fonder. Live a little more separately, try not to think about when you last talked, be your own person, and things will work out if they are meant to. If spending a little time apart gives you more meaningful things to talk about next time, then great. And if spending a little time apart makes you realize you don't really feel like calling the person, then it's good to find that out. Don't push it or it will never work.
I am a girl with sort of a "guy brain" about these things. I like talking to people when I have something to say, and I HATE HATE HATE calling people out of obligation. It means a lot more to me when I have a story I want to share, or when there are things to catch up on.
You said that you hate being a paranoid girl. May I ask you what you are paranoid about? Are you afraid of what he's doing when you don't talk to him every day? Are you afraid of the reason why he might not feel like chatting all the time? The truth is, you should never let someone run your life this way. Be confident, be independent, and be true to yourself. Instead of worrying and waiting for someone to call, go do something that you enjoy. Live your own life. Not only is independence attractive, but it gives you strength. If that person decides to flake out on you, you'll be better off because you weren't depending on them for happiness.