Paint fumes (as well as smog, ammonia and many other chemical fumes) can certainly irritate your lungs.
The inside of your airways are made up of mucus membranes (like the inside of your mouth, for example) and are very sensitive to irritants such as those listed above.
When they are irritated, the can swell slightly and try to get rid of the chemical by coughing. They may burn or itch as well.
Next time, since you know you are sensitive, you could try wearing a face mask similar to those a surgeon would wear in the operating room. You can buy this at Lowes or Home Depot, etc. You should also make sure that all the windows are open and you have a fan going. This will not only help the paint to dry more quickly, but will make the chemicals less concentrated in the room. Lastly, you should take a break at least every half hour--just 5 minutes or so outside breathing fresh air.
I'm glad to hear that you're feeling better.
I hope I've answered all your questions. If not, please ask and I'd be glad to clarify. You're not expected to pay for an answer until you're satisfied.