Did I have a panic attack?

The last two days at work I've had a few 10-15 minute periods were I feel really sick, my chest and throat feel tight (but not wheezy), my hands start shaking and I can't concentrate at all and just feel well...panicky, because I feel so horrible.

I've never had anything like this before, does it sound like a panic attack or something else? What can I do about it?

Panic attacks are normally characterised by hyperventilating (perhaps you had this when your throat felt tight?) and normally include a feeling of fear of death, difficulty breathing, greatly accelerated heart rate and inability to concentrate on anything else. It sounds like you had some kind of panic attack, although it could be an anxiety attack, which is similar - just remember that panic attacks cannot hurt you, and is simply a natural bodily response. As I learned this, I stopped having them, although I do tend to hyperventilate on occasions. One way to combat this, if possible is to treat the root of anxiety, or if it happens for no apparent reason (as it can do) then the best way I have found is to simply try and take deep breaths, lie down, and your body will eventually calm itself. It may also be due to stress - I once had a period of 3 days where I felt pain in my lungs and had to constantly consciously breathe (not like when you think about breathing and do it consciously momentarily - I had to literally think about breathing since some kind of passage felt blocked) but it turned out to be extreme stress, and "climaxed" in a heart attack.