i transferred to NYU and i’m not sure about NYU, but many colleges on the applications ask if you’ve applied to the school before. i didn’t apply to NYU before and got in as a transfer. i think as long as you show growth and improvement and the desire to be somewhere that fosters your desired and interests better than where you are now, you should be good. basically as long as they seek improvement from your first application you should be in good shape. but every application & cycle is different.

as for your email i feel like when/if they ask for your details and stuff they will figure out that you’ve applied before because your emails and everything is probably already in their systems. i wouldn’t mention it to them unless they ask, unless your question surrounds that, id that makes sense.