Sometimes, people don't really scream, but they sing-scream, but I don't know if there's a verb for that. Is there? Because saying screaming is not precise enough in my opinion, so there must be a better more precise way of expressing it. If you don't know what I am talking about, watch the video above.
Belting or vocal belting is a term for singing that overlaps with a yelling/screaming tone, which is what seems to be going on in that video. You also see it informally to describe people who are singing loudly, sometimes with the preposition "out."
Both of the following would work:
"She belted the national anthem."
"She belted out the national anthem."
In genres like heavy metal, the vocal techniques they use are generally just called "screaming" or "growling."