Two important steps
1. Eliminate or drastically reduce mucous-forming foods from your diet. This means diary, soy, meat, etc.
2. Try using a neti-pot. Within a few weeks you might be amazed at how much clearer your nose will be.
Until you get your nose clear all attempts to breath through your nose are going to be somewhat in vain I think. I have the same problems (and have been a lot worse in the past) so I can relate. Try #1 and #2 for a month and report back to us.