Kelly don't give up, shame on your co-worker its not like you are affecting the quality of his/her life by asking them not to wear scent, but it is affecting the quality of your life when they do.
Well Sara I'm glad I don't have to work with you because you can't always avoid those people trust me I have tried, many like Kelly's experience will walk right in anyway and it only takes that 1 or 2 second exposure to cause the migraine/asthma attacks. I'm glad I work with considerate people and I hope you never experience having to ask someone something because it affects your life and get the response that you would have given to someone who asked you not to wear perfume.
If they can ban smoking because it affects other peoples life they should consider banning scents if it is affecting other peoples lives.
There are now 3 people in my office who suffer from scents like I do so it is on the rise and will continue to do so. Just consider there are 600+ ingredients in those products and many of them can be found in your gasoline tank. Read the MSDS sheets on many of those ingredients in your perfume/cologne and you will see "AVOID SKIN CONTACT" "AVOID BREATHING VAPORS" and on and on.