tape your right arm to your body
box for like a week with only jabs and straight leads
that should do the job with a regular program - just go through all the normal stuff with only your left arm.
the required boxing program at west point does a good job with this - the only authorized punch for the first half of the class is the jab. the first fight evaluation is with the jab only. it teaches you to use your right when the time is right...
i also got the extra practice of only being authorized the jab while my sparring partners could use the cross, hook, and uppercut - it taught me how to use the jab effectivly for offensive defense.
calmness comes with experience...take deep breathes, you're not gonna die, it's just a match have fun.
oh and..thinking during a fight=bad
that's why you got a trainor