Looks like a ruptured cyst. I had the same thing happen to a female dumbo HM and she healed up perfectly fine after it fell off. Her's started as a darker area, then a small bump and finally the skin opened up, the cyst fell out within a couple days and the skin closed over the wound. I did give her a couple Methylene blue baths to prevent infection but other than that just the usual water changes.
This is when it ruptured, looks horrible but she didn't behave any differently when it happened.
Give him a couple weeks with a few extra water changes and I bet he'll be just fine. Keep us updated!
Thank you. Its good to hear you don't think he needs meds. I haven't had luck medicating my bettas in the past. Hewey is acting okay, otherwise. I usually do two water changes a week at 35%. Do you think I should increase the water changes? He is in a 5.5 gallon, heated tank with a sponge filter. He is about 2 years old if that helps.
Update: It's been two months and Hewey looks worse. Now, some of the white part is hanging off of him, like it is going to fall off. There is now a red dot as well. I don't want to medicate him if it's not necessary. I have API Erythromycin on hand. I know betta a are sensitive and I don't want it to kill him. Any thoughts? Here is a new pic.
You should definitely not treat fungus with Erythromycin. It's an antibiotic that will kill bacteria but it can actually make a fungal infection worse.
Wait a few days and see if the white bit does actually fall off- if it does, that's good. If not, you might consider an antifungal.
For the time being, adding tannins to the water would help him to heal. There are many ways to get tannins into the water- I personally use Almond Leaves aka Cattapa leaves, and for a sick fish I would actually use organic Roobois tea. It will make your water look brownish red, but this is a good tonic that can help him to heal.