I got to experience this sensation in a training environment. As I went through the Police Academy, we did some simunition training (equate to high tech paintball for those who have never heard of it). The first time I got all geared up and put the paint-shooting Glock in my holster, I went through similar reactions. We also had to wear a helmet/faceguard that wrapped around my face and below my chin. First scenario, and I'm having trouble breathing, chest is tight, hands a little shaky. THEN, my instructor told me to go in to the scenario
Open the door and BOOM, instant tunnel vision.
The good news is that we did several more scenarios throughout training and each time my response was less. I think they called it "stress innoculation" or some fancy term like that. Basically, I reacted more calmly and with less side effects each successive time.