It’s certainly understandable to feel that way. It can be hard not to hear from someone you care about. On the other hand, I think you might try giving him a break here. I’m sure he doesn’t enjoy not hearing from you either, but during work, he needs to focus on his job. I certainly don’t think you’re being clingy! But I do think that if the situation was swapped, you might appreciate some understanding on his part of not being able to talk all the time.
Is there a way you can compromise? Maybe have good long skype dates on Wednesdays, or facetime after he gets off work? That’s a better way to communicate anyway — you feel more like you’re with them — but won’t require him to multi-task with his attentions while he’s getting paid. Maybe he could call you on one of those breaks during his shift?
Talk to him about this! I’m sure you can come to a good agreement that suits you both!