It is not unusual to feel this type of reaction. You were born with a stress- fight or flight response. This is how our ancestors survived.
But, that same built-in response doesn't fit in your world.
First of all, there is cognition. That means, how you define things that stress you. Is it rehearsal or a real tiger attacking you? No, it is just a rehearsal, and remember the play you did before, everyone said how good you were? So, this is just another "good rehearsal" deal.

Use the methods the singing teachers use: Count your breathing silently to yourself: Breathe in a count of four, and out a count of six. That way you are relaxing longer than you are contracting. Practice this as much as you can. Now your body stays in a relaxed mode most of the time. Anytime you feel stressed, just count again.

Most of all, remember, what you have is natural, normal, and okay. I see professional actresses with the same problem, and counting their breathing works for them too.