Hey Jake, I suspect you really do stop breathing when this happens. By the time you get out and breathe again you really are "drowning". There are two things you need to work on:
1. The underlying fear of strangers and your self-consciousness
2. Your breathing
There's not much I can say about the first issue. You'll need a professional for that.
But you can learn to use your breathing to calm you and cope with the situation rather than simply to stop breathing. This is a form of panic attach and if you learn to deal with it by breathing slowly and in a regulated pattern you'll be more than half way to a solution. The problem might go away completely if you can learn to cope with it like this.
There's a system called Breatheasy which teaches you this pattern of breathing by combining it with music. You can get it on mp3 too and carry a player wherever you go. Use it to deal with panic attacks. It works great.