Thanks for your question on Health Care Magic. 
I can understand your concern. 
No, pain is not due to air pockets. 
In my opinion, you are mostly having 
pleuritic chest pain. It is seen with 
pleurisy (inflammation of pleura). 
Chest pain on coughing, sneezing is characteristic of pleuritic pain. 
Most common cause for this is 
lung infection (
pneumonia). 
So better to get done chest x ray to rule out lung infection. 
You may need antibiotic, anti 
histamine and anti inflammatory drugs. 
Don't worry, you will be alright. First diagnose yourself and then start appropriate treatment. 
Hope I have solved your query. I will be happy to help you further. Wish you good health. Thanks.