FWIW, I have asthma which is triggered by riding up steep hills, but with daily medication and regular training I rarely have a problem with it. For me the key is to slow down my cadence on the hills. It means I will never be fast, but slow+breathing is better than fast+not breathing any day of the week.

For the mental aspect, music works for me. I was struggling up the hills on my second Livestrong ride when a song popped into my head. (It was the Foo Fighters' "All My Life.") Having that tune stuck in my head really helped me finish the ride. So now anytime I start to struggle while riding I will think of a good up-tempo song, and if I'm alone I will even sing it out loud.

Good luck!!