Can My Employer fire me for missing one day of work, due to having pink eye?

I am a part time waxing technician, so I interact with clients and employees all day long, I got pink eye a day before I had to work. The pink eye was still pretty bad when I went into work. One of my Co-Workers expressed to me that I should not be there with pink eye, especially because my jobs consists of me working with clients.. Although my employers policy is that "if you are sick you have to find someone to cover your shift, if not then you have to work". I was unable to get anybody to cover my shift, so I left work.. My Boss now wants a Doctors Note. I have medication for pink eye that I am applying, and do not want to spend money on a Doctors Note. Can My Employer fire me for this?? My next scheduled work day is in 5 days, I am sure I will OK to return to work then..

Can they, of course they can unless you have a union contract or a personal contract for employment. Will they most likely not if they were aware that you were sick.

In fact if you had pink eye, they should have sent you home, because of the liability of the business. Did you inform the manager when you went to work