I understand where you are coming from, but being next to people who are sick or have a cough is inevitable in life. Just bring some sanitary wipes and hand sanitizer, use those when you feel someone has coughed towards you. And just avoid people who are constantly coughing so that you dont by chance get the cough yourself.
Try Zoloft for OCD it's been a lifesaver for me the differance is night and day. I had OCD so bad I would clean my small apartment 2-3x a day for hours and hours I stopped eating, sleeping and working to futill the need to clean but it was never ending until I went on the Zoloft Good Luck hope it helps!
To be honest I have the same issue and I probably have ocd but I can't take the medications used for it because I have the bipolar aspect of schizoaffective and they are also anti-depressents. But when I did at first they did improve the symptoms one of which was that. I still have the same issue now regardless of my recovery from schizoaffective disorder. When someone coughs or sniffs I feel disgusted and contaminated. I avoid public bathrooms for the same reason. But this is all part of ocd. Standard anti-ocd medications (usually SSRI anti-depressents, Prozac through Luvox) can help on ocd and behavioral therapy is good as well. Talk therapy is good in general but for ocd targeted behavioral therapy is better. Those can help you get over that feeling but speak to a psychiatrist about the issue and they can find an exact diagnosis and treatment.