Brainstorming, or Perhaps Second-Guessing

Okay, so I'm writing a Harry Potter AU, set pre-Hogwarts. At this point in the story, Harry is nine. He does some accidental magic due to panic, the consequences of which freak him out (the details don't matter). This Harry doesn't know anything about magic, he thinks it's psi powers. But as I said, this particular thing freaks him out, and he wants to ensure he doesn't do it again. But as it was accidental, he can't be sure he won't. So what can Harry do about it?

His resources are:
* the public library
* his primary school?
That's about it.

Any ideas about what he could do? Could he train himself not to panic? How? What about mental disciplines? Is there something he could learn out of a library book? If so, what book or books? This is set in 1989, remember.