It's likely your pup is just starting to come down with something, like an upper respiratory infection or something similar. She may have been running a fever a few days ago which made her vomit. You want to keep a good eye on her, as any lethargy that continues should be checked by a vet, and taking her rectal temp at home is also a good idea (normal dog temps are 100 to 102.5).
As for the eye, if attempting to treat at home you want to be very careful first of all that the eye continually looks better through treatment, and no signs of rubbing at it, reddening worse, or cloudiness appear in the eye.
You should rinse the eye with sterile saline, like that found in regular contact lens solution, and do not let the tip of the container touch the eye. Make sure it is not the disinfecting/storing type of contact lens solution, just the normal saline/ NaCl. You can wipe around the eye with the saline soaked on a soft cotton ball or gauze, but don’t use anything harsh like paper towels.
You can also find a pet safe ophthalmic antibiotic ointment at most pet supply stores, catalogues, pet stores and some pharmacies: like terramycin, triple antibiotic (neo/poly/bac), etc. Ask the sales people if you need help, but it does need to be safe for the eye, not a topical one for skin. After rinsing the eye, apply the ointment 3 times a day (every 8 hrs) for 10 to 14 days.
It can also be bought online, here is a link of just one sight that sells it, if interested:
This is likely conjunctivitis, but could also be a scratch or ulcer forming and if not starting to clear up in a couple of days, you'll need a vet to check it. It is also very possible some debris or dust settled in your pup’s eye, causing this problem.
Best of luck, and let me know if I can help further.