What you're describing sounds like claustrophobia, and the reality is it's pretty common. That feeling of being trapped with no way out is the core of the fear - it has nothing to do with whether there's enough air or not. Most people experience something like it to some degree, so you're not alone in this.
As for whether you should see a therapist, I'd say it depends on how much it limits you day-to-day. If you're avoiding elevators or enclosed spaces and that's making your life difficult, or if it's generating anxiety that's hard for you to manage, then yeah, it's worth talking to someone. It's not a whim; phobias are real and they respond well to treatment. There are techniques that work pretty well for this, from gradual exposure to cognitive behavioral therapy.
Day-to-day, simple things like controlled breathing or finding a focal point in the room (a window, a plant, something to focus your attention on) can help you feel less trapped. But if it's been a significant problem for years, it's probably worth investing in professional help.