Looks to me like a wound that might have become infected.
If you can get your hands on some eSHa 2000, I would use that, and in the meantime if it will take days to arrive, focus on heavy water changes, and perhaps try salt treatment, since that can have anti-bacterial and anti-fungal affects. However, cories can be sensitive to salt. Some have used it and said their cories were fine, others have said their cories have freaked out when salt was added, so it's a personal decision about whether you want to try it. I recommend eSHa 2000 because I've personally had it work with cories, but their problem wasn't as severe.
If you do decide to go with salt treatment, add it very slowly and very diluted at first, and monitor the fishes' reaction to it. If they freak out, then water change with fresh water to dilute out the salt again.
Wish I could help more! Please update us, whatever happens.