My 13 year old cat seems emaciated, I think she is dying?

She used to be overweight now she is extremely thin and bony and eats very little. In the past week she has really gone down hill. She just sits around looking sad. Her eyes have been infected on and off, too. She wobbles when she walks to her litter box. She never washes herself anymore and she looks awful. Should I have her put to sleep?