I like
Caroline and
Carol better, but
Carolyn is fine. I like the nickname
Carrie because it seems the most natural. Other than Caro (which I'm not crazy about because it makes me think of Karo syrup), I think a case could be made for the nicknames
Cara,
Lyn, Lynnie, Ro, Cally, or Arrow. But I think when nicknames aren't typical or obvious, it's better to let them develop naturally, like when a sibling can't quite pronounce the new baby's name and the name they call the baby evolves into the nickname. If my name were
Carolyn, I think I'd just go by the full name.