Forced to sit next to extemely contaigous coworker.

I work in a call center environment. I was forced to sit next to a person who had just come back from long term disability suffering from some kind of horrible respiratory illness. She was out for three months. Her coughing was almost nonstop throughout the day, and her cough was so unnerving sounding that it made me feel very uncomfortable and afraid to sit next to her because she sounded extremely contagious. I ask her supervisor if they could move her away from me several times and was told no. I also asked my supervisor if I could be moved away from her and was also told no. As a result of sitting next to her I came down with Pneumonia and laryngitis which caused me to miss almost three weeks of work, all of which is was authorized and documented by three doctors.
My question is: Can I sue my employer for forcing me to sit next to this very contagious person? Not only did they put my health at risk, but also my family�s health and other employees who may have been exposed to this extremely sick person who by the way, is now out of work again.