I Am A New Mom And Have A 19 Month

I am a new mom and have a 19 month old son. He's very smart and almost seems a little older than his age which means that he's recently started to throw some really bad temper tantrums. He screams so loud and cries so much but never bangs his head or face, still there's always blood in his mucus or a little bit of blood around his nose after a tantrum.. Is this normal?