Hello, new member here, I just thought I'd add to this thread as we just went through this.
My 8yr old brindle buddy took close to two months to heal from an eye ulcer. It was a real crappy time for all of us. Eye ulcers will not eventually heal by themselves. They are painful to your dog and will only get worse if a vet ophthalmologist does not intervene. Antibiotics & eye gels may help, if caught early enough, but my guy went through two eye surgeries on the same eye (4 weeks apart), accompanied by 3-4 types of eye drops, 3-4 times a day. He also had to wear a headcone 24/7 for the duration of the treatment.
The eye ulcer can be healed, it just takes time and alot of patience. The vets at our clinic call them "Boxer Ulcers", as they are so unfortunately common to the breed.