Sounds like transference (from you) and countertransference (from your T). Which is very common, so I guess you could call it "normal." My T has admitted to having some maternal-type feelings toward me, and I have a bit of maternal transference for her, too (not anywhere near the paternal transference I have for my marriage counselor--not sure if there's countertransference there or not, but probably at least a little). In a way, it's nice to know she cares for me in that way. But I also see how it could be weird or scary if you're not used to having people care for you like that, particularly people from childhood (like your parents).