Hello and welcome to Just Answer. I am a licensed veterinarian and would be happy to answer your questions.
Is the eye discharge a new problem as of last night as well?
Is there nasal discharge?
How long has she been lethargic and not eating well?
Can you check the color of her gums and see if they are nice and pink and if the color comes back quickly after you press on them? Are they wet or tacky?
I noticed the eye discharge this afternoon after she finally woke up to go outside since this morning.
She has just been lethargic since this morning. She showed no interest in getting out of bed for her morning walk, she is usually very active and excited to get moving in the morning. I haven't seen her eat anything today, and usually she grazes all day from her dog food.
Her gums are pink and the color comes back quickly after I press on them. They feel tacky.
It sounds as if she is perhaps a little dehydrated, but that is not too surprising if she is not eating well and is lethargic. I am not sure if the eye discharge is related or not and it worries me a lot less than the lethargy and cough. Dogs can get upper respiratory infections, but they aren't usually severe enough to lead to lethargy or changes in breathing. Eye discharge can be due to many causes including irritation, bacterial or viral infections or even changes or decrease in tear production, but that should not lead to changes in breathing either.
If these symptoms continue, I would definitely have her examined by your veterinarian. It would be prudent to have her chest xrayed if this abnormal breathing continues. Although it sounds like it is a respiratory problem, we cannot rule out a heart problem with the eye involvement being unrelated.
Good luck with her and please let me know if you have any further questions.