Does suffocation pain involve nociceptors?
This is more of a hypothesis



I am not sure if suffocation per se would cause pain. Asphyxia, as RoryM indicated in their comments, can lead to anxiety and panic but not really pain. However, forceful breathing may lead to muscular fatigue which may result in pain. Pain induced by muscle fatigue is called myalgia. Myalgia is possibly triggered by low pH generated by lactic acid, via ASIC3 (Acid Sensing Ion Channel) receptor. Carbon dioxide has no role in this process either directly or as a synergist. 


Reference:

Alan R. Light, Charles J. Vierck, and Kathleen C. Light. (2010) Translation from Mouse Sensory Neurons to Fibromyalgia and Chronic Fatigue Syndromes. Boca Raton, FL: CRC Press; Chapter 11 (Myalgia and Fatigue)