Whenever the gills get swollen open like this, it's a great idea to start treaating for flukes, as they are very likely to attack the gills, and if you let them be there for long, it will easily lead to the death of your fish. There are also gill worms available, they look like small, white maggots crawling around on the filaments of the gills. Which are of course another kind of parasites that you need to treat for.
Here it looks a bit more like some kind of fungus though, but treating for both fungus and parasites isn't too challenging, so if you'll only get started asap, your fish should be okay
Now, I would first of all like you to take a look at his second gill, is it a healthy, meaty red? Or is it paler, darker or spotty? If it is darkened/pale you can easily add a bacterial infection to the problem. (Just in case you'd have a microscope, a gill biopsy would be wonderful to determine what's wrong with your fish! You could take a small sample of the slime under the gill cover and look at it in the microscope. If it's streaky and looks hairy, it's fungus, and if it looks like some small organisms or "balls" you can easily consider bacterial infection or parasites as an option
What I'd do now, would be buying the appropriate medication against fungus and parasites. There are certain medications available against many kinds of parasites that would be a good idea to buy, and of course, anti-fungal medication. If you want to, and especially if you'll notice spotty or miscolored gills, it might actually be good to buy a broad-spectrum fish medication and go for the "shotgun method". But only, and only IF you see miscolored gills. Just to be on the safe side, I'd buy some medicated food against parasites, since flukes (if they're present) are very hard to get rid of.
Before starting to treat, you need to make sure that you have a water test kit containing tests for pH, ammonia, nitrite and nitrate, be sure to test it every day during treatment, so you can be ready to change some water when needed. It's crucial that your fish has pristine water quality in order to recover better.
Remember to observe your fish! To see that he's getting better. Good Luck!