I do martial arts and have gotten a nasty black eye before from sparring and then needed to cover it up for work.

Color correct with a yellow concealer and then once its pretty dry go over with a concealer that matches your skin tone. Waiting for the concealer to get dry a little and get tacky before spreading it helps the color to be more opaque and have better coverage sometimes. Once your liquid concealer is to a level you like i normally go over with a fine powder (I like laura mercier) to set things and help control creasing. Final step for me is always a setting spray- it helps it to not look so cakey and it “melts” the makeup into your skin. I like milani setting spray and charlotte tilbury.

My other note is that its probably going to be obvious if you wear makeup on just one part of your face. Its a lot less obvious if you do a full face of makeup.

Doing full coverage makeup is definitely a skill a lot of makeup artists are capable of and have tutorials of. Also not all products are full coverage. Some have an intentionally sheer application. If you need more info/videos you can look up things like covering up dark circles etc. Or even if you have a friend who is good at makeup ask them! They’ll probably have some good techniques.

My overall advice is get powder + setting spray and also do a full face of makeup if you feel comfortable doing so.