Dr. Artour Rakhimov (NormalBreathing.com) explains a simple breathing technique that has been used by more than 150 Russian doctors to stop bouts of chronic or excessive coughing at night - http://www.normalbreathing.com/stop-coughing-naturally.php
The exercise involves breath holding and reduced breathing to accumulate CO2 in airways and reduce bronchospasm. Most people find that they can have 3-5 times less coughing. To stop night cough, it is also important to prevent mouth breathing (find mouth taping technique instructions) and supine sleep. Good quality of air also crucial to prevent night cough.
Moreover, this breathing exercise also improves oxygen delivery to tissues and organs of the body. This helps to reduce inflammation and stimulates the suppressed immune system. Therefore, this exercise is an excellent cough treatment - http://www.normalbreathing.com/best-cough-treatment.php
. Hundreds of doctors in Russia applied this exercise on people with asthma, COPD, bronchitis, cystic fibrosis and many other disorders with great success.
Note that deep breathing does not increase oxygen levels in cells. First of all, overbreathing or breathing too much air cannot help even with improved blood O2 content since very small normal breathing (6 L/min at rest with 10-12 breaths per minute) provides nearly perfect blood oxygenation in the lungs – up to 98-99 %. The main initial effects of overbreathing are low CO2 in the lungs and that causes reduced oxygen delivery to body cells.
All these effects make physiological sense since CO2 is a potent and natural cough suppressant - http://www.normalbreathing.com/co2-natural-cough-suppressant.php
Thousands of people with asthma, cystic fibrosis, bronchitis, and other respiratory disorders already benefited from this easy respiratory exercise and were able to stop night cough in 2-3 minutes. The exercise is useful since modern medication for coughing is ineffective.