Yes, it's true. You should not try to swim close to sharks if you have a wound that is bleeding.
This blood-smelling ability is often a bit exaggerated in movies an TV-series though, and a single blood is not enough to attract a huge pack of sharks. But with an open wound, you could potentially attract sharks from pretty far away, as long as the water currents are strong.
You know movies they tend to exaggerate a lot. But yeah I guess a single cut couldnt attract a lot of sharks unless youre bleeding to death. But sometimes I get too paranoid when I get cuts from swimming or cliff diving I will stay out of the waters as possible. Talk about being influenced by shark week.🤣