Willing Pilot
Labels in notes are indeed a problem.
You are over 16 and so in medical terms you are able to consent to or refuse treatment in your own right and to discuss your medical problems without involvement from your parents.
go and talk to your GP and tell him why the label is a problem. Invite him to review the diagnosis. If you are not happy simply get a new GP
Asthma is reversible airway contractility so to be absolutely sure you have asthma you need to measure the peak flow (a simple blow in a tube machine you can buy from a chemist for a few pounds) and demonstrate it both falls and goes back to normal. In the absence of such readings and if there is no good history, the diagnosis, for this arguement, can be questioned. Asthma was massively underdiagnosed and a lot of work went into educating doctors to 'think asthma' with the result that I see lots of questionable labels. The CAA medical bods will not be ignorant of this!
good luck