I also get this. I did put a question on here last year, don't know how to post the link though.
Mine started about six years ago when I was driving, and I suddenly realised I wasn't actually breathing! Since then, if I think about it I have to keep taking really deep breaths as you describe. I went to the doctors, and they suggested it may be mild panic attacks and also suggested the paper bag 'cure'.
Mine is always worse when I am in the car , but if we have the radio on and sing along it takes my mind off it.. Also if I can't get to sleep I become very aware of my breathing and take ages to calm it down! Drives you mad, doesn't it?
I try and think of something else to take the focus off the breathing.
Good luck - it's nice to know I'm not the only one experiencing this.