I've had exercise asthma my whole life, but always just treated it with salbutomol if it flared up. I was pretty cavalier about it and just down played the effects in my head.
It took a pretty severe asthma attack on a 360km ride this summer to force me to take it seriously. I'm now on a preventer (clenil modulite) which has properly transformed my riding. I have no idea why I resisted going on a preventer up until now, but it's helped so much on intense efforts. Now it's not my wheezing lungs which slow me down on hills, it's just my legs.
On a non cycling note, I find my breathing is far easier and deeper in everyday settings. I always used to feel short of breath when trying to breathe through my nose but that's a non issue now.
So yes - see a doctor, stick to a preventative regime which works for you and you'll be much better off.