You might try breathing in slowly while you count "1...2...3...4". Then hold your breath while you count "1...2...3...4". Then breathe out slowly while counting "1...2...3...4" Do that several times (OK, do it 3 times, if you want an exact number) If holding your breath until the count of four is too long then shorten it: try "1...2", then start breathing out.
Concentrate on your breathing. Just think about that and nothing else. Feel the air blowing trough your nose, feel your stomach and chest moving. Focus all your attention on the sensation of breathing.
This will help you to stop focusing on the causes of your panic, and will slow down your heart rate without you fainting.
Afterwards, if you can, you might sit somewhere quiet and maybe read something escapist if you have any books that you get completely lost in (or a special interest that makes you calm). That will keep you calm for a while longer and keep your mind off anxiety/stress factors. You want to bring your whole system down to calmness, not just make a temporary dip in your high arousal state.
I do something like this everyday on the train, going to work. It helps calm my nervous system and I don't think obsessively about work for the whole train trip because I am lost in the fantasy world of whatever escapist novel I am reading. Trying regular breathing with "mindfulness" (switching your attention to concentrating on the breathing and nothing else) is a way to prevent panic attacks too - at least, to keep your arousal levels lower at peek stress times, so that little things don't push you over the edge. I am starting to do a similar exercise at lunchtimes, and short relaxation breaks (e.g. less than a minute) occasionally during the day, usually when my computer tells me to take a short break from typing.
PS: I am most likely to feel panic when I am suffering sensory overload. Putting in earplugs (actually earphones attached to an mp3 player) helped me to be less stressed and panicky in that situation. Prevention is better than cure.
Just search Google for "panic mindfulness" and you can read a lot more for free about how to manage your emotional state. If you are good at research, you can find free material on the web to help you. My therapist is using mindfulness to teach me how to manage my emotions and stress levels, including stress from sensory sensitivity.