My Max has extensive experience with eye ulcers and scratches. Cool, fresh air helped his eyes heal. Heat makes things worse. I discovered that if I carried him around outside in the cool air of morning or evening, his eye healed quickly. I carried him so that he wouldn't stick his face in grass and other things.
The other thing that I learned is to put off bathing his head for at least 2 to 3 weeks. The newly healed cornea has to strengthen -- especially if it is a big ulcer. Max's worst one, I waited a month to fully wash his head. Instead, I gave his head a kind of "sponge bath" with a damp wash cloth.
Best wishes to your doggy for a speed recovery.