I think that one can see stress as being evident for both Echo and Narcissus in their sad meeting. On one hand, Narcissus experiences stress because he is not enchanted by Echo. He sees her running after him, throwing her arms around him and being ready to share that which is in her heart. It could be seen as stressful because he is simply not ready for it. There is little evidence that he is in love with anyone or anything and this becomes clear when he rejects her. The stress he feels is being overcome by the moment
The stress that Echo feels is both of the moment and outside of it. Echo's stress results from being unable to communicate that which is within her heart about Narcissus. Echo, the eternal chatterbox, had suffered condemnation from Hera of being able to only recite the last couple of words said to her. Being deprived of her gift of gab, she is unable to speak to Narcissus all she feels and the love she has for him. When she encounters the beautiful youth with her inability to speak, to do what her purpose in life has been to the one she loves the most, stress is evident.