Sweet's syndrome (SS) is an autoinflammatory condition and is caused by errors in the innate immune system. There is no evidence to show that it is directly caused by stress, but stress could possibly exacerbate conditions that affect the skin.
WebMD has posted some information on how stress affects the skin - 'The Effects of Stress on Your Skin' (features comments from Nina Goad of the British Association of Dermatologists, and Consultant Dermatologist, Dr. Anthony Bewley).
Does anyone find that stress makes their SS worse?
In my case, my SS flares up whether I'm stressed or not, but I know that everyone's different.