Does my cat have asthma or allergies?

So I’ve seen our cat do this a few times. He loves playing inside bags, and we prefer him not to be in plastic bags for obvious reasons, but Walmart had these new nylon mesh bags and so he went inside it like a little cat hammock. I put him on the ground so he could play with it and get out whenever he wanted. Today he got out of the bag and started doing this. To me it sounds like wheezing, I’ve been wondering if he has asthma or allergies. Eventually it turns into retching, and then goes back to wheezing again. The last time I can recall him doing it I took him outside to explore a little on a harness and leash. He wanted to go under the short deck where there were some rotting leaves. It’s a small space so I didn’t want him going in there and he started wheezing then too. I’ve seen him do this maybe 5 separate times before, this time was the first time he’s ever done that after being in a bag. But that bag may have also been outside for a bit as well as we had put some water bottles in there to take outside for a BBQ we had in our backyard yesterday. So I’ve been leaning towards probably some allergies. It doesn’t ever last for very long maybe a minute max but it still worries me. Any thoughts? Should we see a vet? I also have a video but I can’t upload it so if anyone needs I can forward and email or I have the video available on Facebook.

Hello!   You have posted this on an extraordinarily hot day in the UK and heat / that clammy 'high-pressure' feeling does seem to intensify in a bag, whatever it is made of.  Allergens are also fairly high in the air at this time of year.  We also have to bear in mind that as far as I know, your cat might have underlying heart problems, for example, which are coped with most of the time but when the cardiorespiratory system is under a lot of stress - for example, when sitting in a bag or in hot conditions or in the presence of an allergen - the signs might suddenly become apparent. So: no concrete answers from me I'm afraid, except to one of your questions;  yes, it is undoubtedly the right thing to get your (extremely handsome, if I may say so) boy to the vets for an examination.  To do so, it may be worth paying a lot of attention to ventilation of the carry-container (a lot of vet practices may have a well-ventilated wire basket that you can borrow). Your vets may also opt to look at the video today if they need help to judge whether it might be an emergency. Wishing you and he all the best.