In order to successfully sue for something, you need to show the court that you, the person suing, was wronged. You would have a hard time showing that getting the job you voluntarily applied for caused you harm.

In theory, someone who wasn’t selected could have damages, but they would also have to prove that it was due to racial discrimination. Being siblings does not mean you have the same qualifications they may be looking for. What’s more, employers are generally not required to verify self-identified race.

I can understand your background isn’t in law, but holy crap I hope you have a much better understanding of nursing than basic law because this comes across as “fourth grader who just learned the meaning of suing someone” level of understanding.