I have a similar issue. It is very hard to live with. I would try wearing a mask to sleep instead of the blanket because a mask will stay in place, but a blanket won't. My left nostril is blocked mostly, instead of the right. I do a lot of mouth breathing when I sleep because not enough air coming in nose and the mask also helps to moisturize the mouth with humid air.

I have had ENTs who have done CTscans and MRIs and examined me. I did have a septoplasty 20 years ago that did not help. Recently I have had 2 ENTs say they don't see anything to do surgically. Then I have another ENT say I need a Vivaer procedure, that my nasal valves are not working right. Then another ENT says I need a turbinate reduction, not a Vivaer procedure, he says the Vivaer would not work on my condition. Then another ENT who says not to have either procedure and sends me to a neurologist for pain issues I have in the nose and the neurologist wants to put a wire in my head to send pulses to the nose lining to deaden the pain.