Two main questions pertaining to acute or chronic bronchitis.?

Okay so recently my friends and I have gotten really worried. Sometimes when I cough really hard, mucus comes up and while I'm coughing my back hurts a lot. But that's not it, after I have coughed like this I have a really hard time breathing for twenty-thirty seconds; to the point that my eyes turn watery and red and I'm gasping for air. It's really scaring me, I mean what if I can't breathe even after thirty seconds? I'm worried if it is bronchitis that it's chronic bronchitis. When I was really little I had so sever bronchitis I'd be hospitalized for a week or less, or bed ridden for a week and such. So my questions are as followed:
Do I have bronchitis even though I don't have all the symptoms and which type?
And if I don't have bronchitis then what do I have (if I have anything that is)?
And lastly how can I convince my mother to get me check by a doctor because she's not to keen on going to the doctors.

My 'deep' coughs have been going on for about one-two weeks.

If your mom won't agree to have you see your doctor, you should see your school nurse, if there is one, to try to convince your mom. Such deep violent coughing and shortness of breath is definitely not normal in someone your age, and could be a sign of chronic bronchitis or pneumonia.