Does he care that I'm so shy?

My advice would be to do something with him other than just talk. Its hard in person especially at first. if you play a game or go somewhere it is easier to talk about something because then you are doing something together and you can talk about it. It is way easier if you get to know him face to face than phone to phone.
Just bring out a game the next time he comes over. If you have other people that you are comfortable around it makes it easier to start talking about anything. good luck
just try something new. he probably wishes that you would open up and talk about anything and everything with him. yeah it bothers him but he won't say so till he can't stand it anymore.

Well there's no way out of this. We've all got to get over our shyness so the more practice you have talking to him in person, the better off you'll be. It's a stage that we all face in our teen years and it sucks, but one day you'll get over the awkwardness. I don't think that it'll bother him now but somewhere along the line it might come up as an issue for him.

lol. I am the same way. its really easy for me to talk to a guy I like on the phone, but it isn't as easy in person! I have no clue why I get like that either. just realize he's going out with you and already likes you its okay to be comfortable around him. it could possibly bother him that you are shy, but not necessarily.