Wheezing when exercising is not uncommon in athletes but there can be all sorts of reasons for it. Possible causes include: allergens in the air (such as pollen, dust, animal hair, pollution), which can irritate the airways, causing them to respond by constricting and making it harder to get air in and out; inhaling cold air can have a similar effect to allergens; some mild food allergies can cause inflammatory responses in the airways; EIA (Exercise Induced Asthma) where exercise itself causes constriction of the airways early on during training sessions; anxiety and stress.
So common ways to combat it are: training in a different environment (free from possible allergens), such as a different gym or outdoors; training indoors on very cold days; systematic elimination of foods that could be causing an allergic reaction (for example, wheat or spicy foods); seeing a medical specialist for an EIA diagnostic test. If positive they can prescribe medication to alleviate and control symptoms.
In terms of why your wheezing is specifically linked to running and not cycling or cross training, it could simply be that running – even at a steady pace – is far more stressful on the body.
It could also be linked to posture or breathing technique – for example, if you’re breathing is shallower when running – so analysing technique and consciously breathing deeply, especially when starting out on a run, may help.
Unfortunately it’s hard to say exactly what the problem is, so the best course of action would be to try the above suggestions, and if none are having a positive impact see a doctor to get a full medical opinion on the matter.