I have a small sample (11 responses) of categorical data. I want to compare a binary response (near vs. far) to a nominal response (disease 1,2,3,4,etc.), and see if there is any dependence.

Chi-square has given me a poor response with expected cell counts below 1.
I looked at the forums, and Fisher's exact test seems only for 2x2s - is that true?

What other tests recommended for such a situation?

Many, many thanks!