This is very common if you have an anxiety disorder or have been prone to panic attacks in the past. As an individual with a crippling form of anxiety, I can say that it's nothing to be ashamed of. Depending on the severity of these attacks, you may or may not want to see a doctor if they persist. Remember that a game is never worth jeopardizing your health.
While there is no one strategy that works for everyone, a great place to begin is by playing with close friends. Try playing with some people you are comfortable with before going up against random players online. Something that helps me is to just intentionally lose my focus. It may sound counterintuitive, but that moment of distraction say before a match can really help. If your mind is somewhere else for even a few seconds, then it's not on the anxiety. After it's passed and the fight has begun, you can regain your focus and by that time it's easier to concentrate on the match and with a little less pressure.
I don't neccessarily think it's a confidence issue. There was a Killer Instict premier at Best Buy years ago that I played in. I was shaking, hyperventilating, sweat was dripping off my face but it wasn't due to not having the confidence because at the time I was convinced that I could pretty much beat anybody who stepped up.. and I did, even if they were looking at me wondering what the hell was wrong.