So he knows he's a narcissist, then. An ex (many exes) will have told him that.
No one fits the profile of a narcissist 100%. They are good at masks, so your narc will seem different, special, have some kind of quality that allows you to doubt.
What you have to go by is their behaviour and your feelings.
Behaviour: love bombing, devaluing, discarding, and (sometimes) hoovering. It's the same playbook, over and over. He'll have other women on the go too. Possibly men too.
Your feelings: it's my fault, what can I do to make him understand, I'm going crazy, I can't cope with this, I don't know what's going on, I'm so confused, I love him, I'll do anything for him, I can't survive this, I need him, he must love me really, maybe he doesn't know how much I care, it's my fault, I'm not good enough for him, I don't know what happened, I let him down, if only I could just explain, this is unbearable... etc.
Feeling desperate and confused and like you can't survive without him, especially when the relationship has been over a short period of time - these are clear signs you have been the target of a narcissist. But even if they weren't, you can't be with someone who makes you feel that way.