Is breathing through one nostril bad? ( is it curable?)

Nasal obstruction that alternates sides is most commonly due to turbinate hypertrophy. The turbinates are often reduced during septoplasty or other nasal surgical procedures in order to improve the nasal airway. The turbinates swell in response to inflammation such as allergens, smoke, etc. If symptoms do not response to medical management, such as a nasal steroid spray, then surgery may be an option.
Be sure to see a nasal surgery expert.
All the best,

Hello Ivan and thanks for your question.Given that the nose and nasal breathing passages are three dimensional structures, a complete examination is needed to determine the diagnosis and the exact reason for breathing difficulty. In our office we used a headlight and other instrument to come up with the exact cause for this issue.  
The following are the 3 main reason for mouth breathing and difficulty breathing through the nose:1. Septal deviation2. Turbinate enlargement3. Nasal Valve collapse4. Major allergic rhinitis5. Any combination of the above.I would highly recommend visiting a few plastic surgeons who specialize in this exacting and artistic procedure. In our office we provide patients with a personalized, individualized and complementary consultation to address these similar issues.
For more information and many before and after examples please see the link below.
Best wishes and good luck.
Dr. Sajjadian