You're right: it's not your job to teach a boyfriend or partner to be considerate and caring. You're not his mother, after all. What his sister said to you was unfair and equally inconsiderate (and chock full of soap-opera drama, to boot).
Moreover, doll, in the grand scheme of things, you're a baby. I don't mean that in a patronizing way: rather, at this point in your life, and when you're just dating someone, in your first relationships, things shouldn't be a huge struggle. You want to deal with struggles years from now in a relationship you and your partner have invested in for years, that's sound and sensible. But this early in the game in your life and dating life? In just dating for two short months? Nuh-uh.
Dating is supposed to be a sort of trial period, where people feel each other out to SEE if theymight make a happy, healthy and harmonious partnership as times goes on.
...and the signs aren't pointing there.