It is not unusual for me to be in a head-down position. It is a useful skill to be able to clear the mask in any position and it adds to your self confidence. My instructor had us start clearing in the head-up position and we slowly progressed to side clearing and finally to head-down clearing.
Take time to think about where gravity is taking the water in your mask, where it will exit, and how to trap air at the high side. It will become instinctive, which is at least half the point of acquiring the skill. For Southern California divers at least, the other half of the reason is lobster hunting. It is also a useful skill for macro photographers.
As for water getting in your nose, try staying ahead of it (clearing more frequently). Can you manage being head down in a pool without a mask now?
Another thought is maybe your mask doesn't fit as well as it could?