In short, an archaic (and then later dialectical) name for any of several diseases of the lungs involving coughing or difficulty breathing. Originally, it would have been the TB -- the word seems to be a Middle English derivative of phthistic (at the time spelled closer to ptisike), one of my favorite words, from the Greek phthisis, originally meaning a wasting away but often specifically in the sense of from consumption. Or maybe the original sense was the asthma, as by the middle ages, the meaning of phthistic was shifting to that. I learned it as the last sense, however -- a tissocky (or tisicky) cough is a thin, dry, persistent cough I particularly associate with late winter in temperate climates.
Mrs. Heald kept to her bed with a tissick to the tubes.