The "ultimatum"

So my boyfriend and I are going through a rough patch right now and he gave me an ultimatum; that if i don't change then he will break up with me. He doesn't think he needs to work in anything inside himself, just me. He says I'm too clingy in public (keep in mind I only hold his hand), I text him too much (10 texts or less a day), and that I'm too lovey dovey sometimes (I do it all behind closed doors)... My question to you ladies is if I should try and work on those things, or just end it?