'Illness' can be an uncountable noun, and 'an illness' and 'illnesses' can be countable singular and plural nouns. 'Illness' means 'illness in general', while 'an illness' means one particular illness. It is equally true to say that unhappy people suffer from more 'physical illness' in general AND 'physical illnesses' which we can name and count.
When you say 'It was a mistake', do you mean 'It was marked as a mistake'? If so, I don't think it should have been. Google Ngram Viewer shows that 'suffer from physical illness' and 'suffer from physical illnesses' are both used (as well as 'suffer from a physical illness').