In Child's Play (1988), when Chucky goes to see Dr. Death, he mentions the pain he is able to feel and the fact that he's bleeding. He says "I didn't think anyone could hurt me." Is he confused by the pain and blood because he thought he'd be invincible after using Death's voodoo magic to come back or because he's in the body of a doll?
Chucky is becoming more human
The longer Chucky's soul remains in the doll, the more human he becomes. At the beginning his doll body was fairly immune to injury. But as more time goes by, the more Chucky is turning into a real boy. And of course, a real body is prone to injury, especially by projectile.
[Chucky goes to visit John.]
Chucky: Hi! It's me, Chucky! What d'you think? The grigri work?
[John nods awkwardly.]
Chucky: You know, when you were telling me all that stuff about how to beat death I thought maybe you were pulling my chain. But not now, uh-uh. Only one problem.
Chucky: This. (Points to a wound below his shoulder) I didn't think anybody could hurt me. But last night I got shot. And you know something? It hurt. It hurt like a son of a bitch, it even bled! Now why's that, John?
John: You're turning human.
John: The more time you spend in that body, the more human you become.
Chucky: You mean, I have to live out the rest of my life in this body? NO FUCKIN' WAY! You got me into this, you get me out!
John: I can't do that, Chucky.
Chucky: Why not?
John: Because you're an abomination. AN OUTRAGE AGAINST NATURE! You've perverted everything I've taught you, and used it for evil! AND YOU HAVE TO BE STOPPED!
(source) Emphasis mine.
So yes, he is confused because he thought he'd cheated death, but is now discovering he's still mortal.
At first, technically Chucky was meant to be immortal, although once he told Andy he was Charles Lee Ray, he had somehow become mortal again with the same weaknesses as any other human to an extent. As Dr. Death said, "You must possess the first person you tell your secret" (I'm paraphrasing).
Chucky even states he must become a kid again. This means that once he possesses Any he shall be an immortal being in a human form (Unless he tells someone else his secret while within the new form). In Child's Play 3 (1991), Chucky implied that since he was in a new Chucky doll (form) he could simply tell Tyler his name and possess him instead.
I assume that since he wasn't already immortal in that new form he must have to switch into another form originally to become an immortal being. Long story short: The more time he spends in the doll form, the more human and weak he becomes.