Hola Tyler, espero que estés bien.
There are “neutral” words that any Spanish speaker will understand such as alterado, furioso, iracundo o encolerizado.
Of course, depending on the Spanish dialect there'll be also a variety of words and expressions, some of them with a wider usage than others.
For example, in México you can say that someone is enojón from the verb enojar but enfadica from the verb enfadar in Spain (both verbs mean to get angry). I believe both are quite understandable to natives, however, the one you decide to use will reveal your linguistic background.
There are also common different expressions:
Spain: Tener mala hostia, tener mala virgen, tener mala leche o estar de mala leche.
*Jeez! I had forgotten the verb cabrearse. People in Spain use this word a lot.
México: Andar enchilado/a as a metaphor for eating spicy food and feeling the heat or Estar que echa fuego with a similar meaning.
I hope I’d helped you.