I used to suffer social anxiety and get panic attacks regularly a few years ago, even just talking to a shop assistant or meeting a friend of the family. It's hard to believe it now as I'm one of the most popular and outgoing people at my university, and it's usually me that puts other people at ease.
Just to explain panic attacks...
When you're nervous you get tense, breathe shallow and start rushing and fumbling. This causes you to lose your breath, your heart rate speeds up, you can get shaky, which all escalates until you start to panic - and even pass out in some extreme cases.
My best advice and something I learned a while ago and which you can practise immediately, and that's to purposely slow down.
When you speak, take time to pause between sentences, breath comfortably (deep from the diaphram, NOT the chest - as Alpine pointed out) and make a point of hearing every word you speak aloud.
However, it's easy to forget to tell yourself to slow down sometimes, especially when you're surrounded by impatient people who talk fast, rush around or don't pay attention, but choose your OWN pace and don't let anyone rush you. You have a right to take your time and move at your own pace. If someone gets impatient, that's their problem! Keep that in mind!
It always helps to practise, which you can do by reading extracts from books aloud, slowly and comfortably, practise moving slowly (pretend you're in slow motion for a while) and focusing on sounds around you helps a lot too.
Seriously, this alone will make a massive difference and stop the panic attacks.
On top of this, you can just try to increase your social activities. The important thing is to feel comfortable in the situations so try taking it step by step.
I know what a restrictive curse panic attacks can be so I hope this helps.