Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Cosmo. I suppose it's possible that a small amount of shampoo might have gotten into his eye despite great care taken by your groomer to prevent this from happening.
As long as he's not squinting nor keeping his eyes closed (which denotes pain and a vet visit sooner rather than later is recommended), then he may respond to over the counter medication such as ones which are listed below.
I'd recommend treating him 3-4 times a day.
The Systane products listed below can be used in dogs, but the ones with vasoconstrictors, such as naphazoline should be avoided. These products are labeled as "taking the red out" or for "red eye".
Tears Naturale Nighttime
Systane Ultra lubricant sterile eye drops
Advanced Eye Relief Nighttime
Akwa Tears ointment
Continue to apply the cool compress as you have been doing 2-3 times a day for about 5-10 minutes.
If the eye doesn't appear to be improving (or worsens), then a vet visit tomorrow may be prudent.
I hope this helps. Deb