Jealous people get angry more easily than people who aren't jealous. So, if your crush has been more moody lately than he usually is, he may be jealous. This is especially true if he gets angry when you are around other guys, when you mention other guys, or if you're dating another guy. He may not necessarily direct his anger at you or the other guy, either. He may be negative or generally unpleasant to other people even though he is jealous of you.
A jealous crush will probably call you, text you and e-mail more than someone who is not jealous. This is because the jealous crush is not just calling to check up and see how you're doing. Rather, she is calling to see if you're with someone else and, if so, who. So, if your crush gets in touch with you more often than she used to, she is probably jealous. This is especially true if you've just started dating someone else.
If you know your crush well, you probably argue with him from time to time. However, if he is feeling jealous, the arguments will occur far more often. This is because jealousy is a negative feeling. What's more, it's a negative feeling that he associates with you. So, his jealousy will drive him to nitpick you more often, criticize you more often and generally argue with you more often over seemingly unrelated issues.
A crush who is jealous will want to be your number one priority. This is not really reasonable, especially because you are not in a relationship with your crush. So, if you tell your crush that you plan on doing something that doesn't involve him, and he gets upset, then he is probably jealous, which is where this unreasonable request is coming from.