Thanks for the input.
I went to my doctor in VT and specifically asked to be checked out for asthma. He had me breathe into a few machines and then came back and said my breathing was perfect. I tried to argue it with him but he was just a 'tests don't lie' and 'hoofbeats are horses' type of doctor. (He actually missed a few other things that my psychiatrist caught just from me vaguely complaining of some symptoms in a session. He ordered all the necessary tests himself, which was good.)
I was told years ago that I'd be prone to adult-onset asthma, too. So maybe it is worth going and making a fuss with the doctor here.
In the meantime, since I'll be going into London tomorrow to sign student loan cheques, I'll pop into Boots and get some cough syrup.
Those machines will only show you have asthma if you are having an asthma attack. If the doctor in VT tested you when you were feeling fine, then you would have the same response as someone who doesn't have asthma at all. That's what asthma is - it's a condition that causes problems breathing when triggered by something else. If you aren't exposed to a trigger, you don't get asthma symptoms.
There is a test that doctors can do to check for asthma if you aren't having asthma symptoms. It involves giving you a chemical will cause you to have an asthma attack, and then seeing how you respond to an inhaler.
Also, asthma will cause your lungs to close up on the exhalation, not the inhalation, which reflects the breathing noises you've been making.
I already knew I had asthma before I moved to the US, so I don't know what the procedure is for diagnosing it in the UK. In the US, they always give you a chest x-ray, to make sure it is just asthma and not anything worse.