A yoga class (or dvd) can teach breathing techniques that will help. I always try to get my breath into an even, slow rhythm, especially while climbing. Of course, I end up huffing and puffing, but I try to slow it down and even out the breath as soon as I've gone over the top. Really focus on bringing the air into your belly, not way up in your chest. If possible, stay seated with your hands on the top of the handlebars on climbs, and try to relax.

As for the runny nose, tissues up your jersey sleeve, down your bra, and in your pockets.