You have managed his emergency very well with cleaning and cold
compress and the antibiotic ointment.
But since it is near the Lid junction and you have mentioned persistent bleeding, it is advisable to have an ophthalmologist look at it.
He might require a suture or two to avoid bad scarring of the tissue on healing and it's effects as it is involving the lids. And an open wound requires further hospital management even though it is an inch.
Take him to your nearest eye doctor at the earliest. Hope he recovers well. Take care.