Could someone get eye herpes if someone with sores in their mouth breathes on them?

No: Herpes flares up in the eyes because it is already in that persons body. You can only catch herpes type I from someone else if you are immunosuppressed. Type II herpes is transmissible but requires direct fluid contact and this is unlikely in an ordinary breath. Also there are many reasons for sores in the mouth and your friend might have one of the other causes.