It's really, really normal, especially at this stage - you've just started to feel baby kick, baby is near or at viability, perhaps you have found out the gender which gives a bit more of an identity, and you realise the days left are getting perilously close to double digits.
I definitely went through this with my first at some point between 20-24 weeks. The whole thing seemed so enormous - I could not imagine anyone calling me "mummy" - that was crazy. And don't even get me started on the concept of breastfeeding.. that seemed utterly insane now that I'd thought about it logically as those things were for shoving in tight bras to get attention, right? Ironically I've actually been breastfeeding her or her younger sister for over 4 years now, aside from a few months off towards the end of my second pregnancy!
We started buying our first baby stuff eventually, and I vividly recall seeing the brightly coloured toy looking enormously out of place in our "adult" living room. Like somebody else's child had left it there. It always felt like it was going to be someone else's baby showing up at 40 weeks!
I felt like that throughout the rest of the pregnancy, especially when we started assembling the pram - that was a weird feeling. And then when DC1 showed up, very suddenly and quickly on the evening of 36w6d it is safe to say I was in shock! But that first night with just me and my baby and it just all changed, as if a switch had been flipped. She was mine, ours - not anyone else's who was visiting - this was the little girl who had been hanging out in my tummy for the last what seemed like forever. She belonged to us and no-one else. She didn't have a clue how to be brought up any more than we knew how to bring her up and so we would all muddle through together and so that's what we do!
Okay, so there were still moments in the first few months where I'd look behind me if someone said "DC's mum" and in fact I still sometimes feel that way.. but it does all come together for most of us. Promise!
And yep, totally normal to worry about the health of the baby. I have never stopped fretting although it doesn't help in my case that I have been high risk for this pregnancy and my last one - but I swear I worried just as much in my first one which was normal!
I had different doubts around the same time with DC2, along the lines of "TWO??!" and I'm 23 weeks now with DC3 and fully expecting them to hit any day now - I'm currently still in denial over having three, see 
Sorry for the essay!!