I dont think it is asthma personally.
All the doctor will do…is test you with a peak flow meter, give you a blue inhalor and send you packing.

I think strong antihistamines could have that kind of side effect,couldn’t they?

Try this link for all asthma related info:

The symptoms of asthma may occur for no obvious reason. They may include:

feeling breathless (you may gasp for breath),a tight chest (like a band tightening around your chest),wheezing (a whistling sound when you breathe), andcoughing, particularly at night

Peak expiratory flow rate test

The diagnosis of asthma can typically be confirmed using a number of tests, the most popular being the peak expiratory flow rate (PEFR) test.

The PEFR test uses a small hand-held device known as a peak flow meter which can measure how much air you are able to breathe out of your lungs. A reading is taken, and you will then be given a medicine which is effective in treating asthma in the short-term. A second reading is then taken. If the reading is much higher after taking the anti-asthma medicine, then the diagnosis is normally confirmed.

You may be given a peak flow meter to take home with you, and a diary in which you can record measurements of your peak flow rate. This is a good way of recording how the symptoms of your asthma react to different circumstances.

If the symptoms of your asthma are different than normal (atypical) or you have additional symptoms, you may be referred for a chest X-ray. This is to rule out other lung conditions, such as chronic obstructive pulmonary disease (COPD) (a lung condition that is similar to asthma, but usually caused by smoking), bronchiectasis (inflammation of the airways of the lungs), or lung cancer.

Exercise-induced asthma

Your GP should be able to identify exercise-induced asthma by asking you about your symptoms in relation to exercise. Common symptoms include a cough (which normally starts 6-10 minutes after exercise) and chest tightness (appearing up to 1-2 hours after exercise).

Your GP will also want to know about any symptoms not related to exercise, such as coughing at night, or breathlessness. This can rule out the possibility that your exercise-induced asthma is being caused by poor asthma control.

Go here, this article and while you are there put asthma in the search on top of the page. that will return a lot of info for you, this is a credible site reviewed by doctors

It would seem if you try an inhaler before exercising you might know, something like albuterol is inexpensive, I use it and it’s about $20 for a pocket size inhaler (generic), of course only if your doctor thinks it worth a try