Hey ho,
I too am part of the "Epic Panic Attack at Work Club"..."EPAWC"?...that don't work, we need better t-shirts.
Uuuuuuuunyway, I was fairly lucky in that I work in an art studio where we have enormous monitors to hide behind and everybody wears headphones, so it went mostly unnoticed with me, but sounds like you are having a rough time of it.
I would echo the above recommendations, if you are feeling emotionally shaky at all during the day, avoid any unnecessary chemical stimulants, and try to clear your thoughts or focus on something menial or simple to get the negative/scared thoughts to try and subside.
Panic attacks can really suck, and if you have one, can really knock you of kilter all day, but if you try to stay aware of your mentality during the day, you will normally be able to feel one coming on long before it becomes a big problem, and react accordingly.
If all else fails, you can get medication from your doctor to stamp them out...not exactly the idea solution IMO but it's worth a thought.
If it's any consolation, I went from having 3-4 horrific panic attacks per day to pretty much nothing. Just takes some time and effort to learn your own coping methods. There is light at the end of the tunnel ^^