I would recommend that you have an ENT look into your nose. This specialist may culture your nose to make sure you do not have a chronic infection in one or both sides.
See a doctor soon.
That i am sure is probably allergies, this is just my opinion i am not a dr. but you should get rid of any animals in the house or at least put them outside alot. Get a clean air machine, and definetaly keep a warm humidifier going as often as you need this will keep your nose from drying up so much. After a week or so you should see a difference. I think your home may be to dry inside. You need moist air.
Mary
Thank you for the responses. I would never get rid of my animals though and I would certainly never leave them outside. They are part of the family. To me that would be like getting rid of my kids. I hope they are not the cause, but if so, I'll have to live with it and take some of your other suggestions. I'm going to make an appt with my doctor. Thanks!