My nose is curved, i.e. the partition between the nostrils is curved on one side. Is this rare? Any treatment?

It causes breathing problems. I have to sleep only on one side to
allow respiration.
It is very common. You can go here to learn more:

http://en.wikipedia.org/wiki/Deviated_se...
That's what called a "deviated septum", and it's not at all that uncommon. Only treatment for that that I'm aware of is surgery, sometimes referred to as "a nose job".