Well, I am not saying I am cool, as in かっこいい. I am not narcissistic. ^ _^ I want to talk about this phrase because it is widely used as a slang these days, especially among younger people, and you must have heard it.
Cool can mean “okay”. So “I am cool” means “I am okay”. It can be both physically, or emotionally okay. For example, you had a fight with your friend, and you haven’t heard from her in a couple of days. You can call or text her and say, “Are we cool?” meaning, “Are we okay? Are we still friends?”