I have the asthma symptoms and problems, but my doctor isn't saying officially asthma, just bronchitis?

For it to be asthma. ...It has to be recurrent, and reversible. If it happened once or twice, and is not responding to albuterol too well, it isn't acting like asthma.
Asthmatic bronchitis. Asthma is caused by an inflammation of the airways - a bronchitis of sorts. Asthma is a possibility particularly if this recurs.