Ok, this falls under the ADA. You get violently ill from smelling that perfume and yet this woman continues to wear it. This is a violation of your health rights - your employer to make a reasonable accomodation for your illness due to that perfume. Have you been tested for this? To have documentation that this perfume is what is causing the reactions? You need medical documentation. Your doctor or doctors to back you up.
You can make a request for the workplace accomodation via your Human Resource Department. These requests should be in writing and should include the following information: Medical or psychological condition and its duration, nature of requested workplace accommodation, and a brief explanation of how the requested accommodation will enable you to perform your job.
You may be asked to provide medical verification of your medical condition from a health care professional to support your request. It may also be necessary to provide the health care professional with the your job description so that your doctor/s can evaluate how the requested accommodation will assist the you in performing your job.
You have a serious health condition and need to find out if your condition is covered under workplace accomodations for health. See the following:
Ed Kit 1996 - What You Should Know about Workplace Laws (US Labor Dept)
ADA Home Page - ada.gov - Information and Technical Assistance on the Americans with Disabilities Act (Department of Justice)