Is this black mold/wall damage fixable without professional help?

That section of the wall must be cut out. The drywall and plaster and then behind it must be cleaned. You would cut out about 12" over the molded area. I see mold too next to it.

Fans help having a huge mold issue. If you have a flood and standing water fans are not the fix though. They just keep the issue from getting out of control.

That whole section of drywall should be cut out and the inside of the wall inspected for more damage/mold. If it's an exterior wall or if there's insulation in there, it should be removed too. Then you need to clean the area with a mold killer. I have used vinegar because it kills surface mold and gets in to kill the roots. Once all that's done, then replace the insulation and do the drywall repair. If this is your unit, this is a good DIY project and there's a lot of information on this site to help you out. If you're renting, check with your landlord about getting the repairs done.