I'm a little bit confused... did you meet this person, have a great time, and then the next day they wanted nothing to do with you? That is how it sounds to me, so my response is based on that interpretation - if I'm wrong, I apologize!

If you only met them the night before, then it wouldn't really be appropriate to keep bothering this person as it means you'd be spending more time apologizing and bothering them than you would have spent in a friendship together. If you just met one day and didn't hang out again, they don't owe you any explanations.

You haven't said what you did that could require an apology, but if you didn't do anything then there is no need to apologize and it's just an unfortunate case of having one person not like the other. If you did do something that warranted an apology, well, they don't have to accept it or give you another chance.

Trying to make them jealous or to somehow force them to accept your apology isn't the right choice, no matter what went on before hand. You can't force someone to keep you in their life, and you can't force forgiveness. Trying to make someone jealous is not a very mature action and also won't result in them giving you another chance in the long run.

How do you know that this person has NPD if you've only known them for a day? Most people aren't super open about mental illness, especially the ones that get a loooot of negative stigma.