I don't think the prince is evil. Nora says that the prince is "only as kind as [Nora] is obedient," but Shuri also points out Nora was passed over for the title of the Sword of the Crown Prince. Nora's already a bit of a jackass, so he's pissy that the Prince likes Jeremy better than him. (Even if the title has not yet been given.)
They're nobles, and nobility is always supposed to favor family over outsiders. The Prince failed to do this, and Nora hates him for it. And to especially lose to Jeremy, because they hate the shit out of each other, stings even worse. That's also probably the reason why Nora took the sword before Jeremy could, because he <i>knew</i> who Jeremy was from a distance, even if he didn't formally meet him.
That's my two cents.