One of my cats had this same problem. It was due to the type of food she was eating. It healed up pretty quickly after I took her to the vet and had them clean it. They also injected the anal sac with antibiotics and pain meds . Having a cone helped a lot too. She couldn't lick the hole which allowed it to heel faster. I would usually clean the hole with peroxide especially after she used the bathroom. This has happened to my cat several times but since I changed her food, it hasn't occured again (cross fingers). That was like 3 years ago.
I don't understand why your vet didn't provide a cone to prevent him licking the hole. I am not sure what type of food your feeding him but one that is high in fiber and a lot of moisture might help with his poo. I hope your Myles find some relief soon. It sucks when our pets get sick.