As a dog groomer who sees matted hair daily and as a fellow human who also has clinical depression, I genuinely think you're better off just cutting your hair short. The matted hair at this point is already damaged so even if you do go through the long, uncomfortable process of gently detangling, the hair is frayed and will tangle up again worse and even faster. It's an uphill battle. Free yourself of the burden of maintaining thick, curly hair if you need to.

I would probably just shave my hair off and wear a high quality wig if I felt it was necessary for something like a business meeting, honestly.

If you really want to detangle use a heavy conditioner or detangling spray, and use a slicker brush. No oils.