What are you using in the neb? Do you know what is causing the severe throat irritation?
I too find it difficult to breathe deeply while nebbing - it generally causes me to cough, but since that is the point of the 7% saline, I just figured it was normal.
When I experience difficulty taking deep breaths, I sit or lie down and do some belly breathing or diaphragmatic breathing - there are a lot of examples on the internet. I cannot speak to specific yoga breathing techniques, because I am not a regular practioner.
Sue