Sounds like you are hyperventilating. Yes, you can be a hidden hyperventilater, that is, you do so but not aware of it. Your explanation suggests that is your problem. Learn all you can about hyperventilation and hidden hyperventilation.
Anxiety or stress can be a cause of this type breathing or your breathing just could be off track for no apparent reason.
Taking deep breaths and very, very slow exhales will help. Do this off and on during the day. Learning how to properly breathe will help.
If breathing properly does not help you need to see a doctor.
Rebreathing in a paper lunch sack would be an alternative to the nose/mouth method you describe. I fastened a lunch sack on a 4" plastic tube (from about 1" diameter candy tubes), put tape on openings at the bottom (they do not glue bottoms very good anymore). Rebreathe 5" off an on during the day and it will reduce the anxiety. (DO NOT USE A PLASTICE BAG, YOU WILL SUFFOCATE). Paper bags allows air to flow in and out of the bag. Plastic does not allow fresh air to enter the bag.
When we hyperventilate, whether caused by anxiety or whether the way we breathe causes anxiety, the body needs a balance of carbon dioxide and oxygen in order for oxygen to be released from red carpusles to vital organs.
Oxygen deprivation will cause lungs, heart, brain to not get enough oxygen to work right. The body needs oxygen in order to function properly.