When something is attractive in an innocent and childlike way, you can call it "cute". Being "cute" is usually a good thing.
But sometimes people try to be cute, and it ends up being annoying instead. The word for this is "cutesy".
A person can "act cutesy":
Don't try to act all cutesy. I'm not lending you my car, and that's that.
You can also "put on a cutesy act". This means to suddenly pretend to be cute.
She puts on that cutesy act whenever she wants something from me.
And some people have a "cutesy look". This means that their style of dress, makeup, hair, home decor, etc. are annoyingly cute:
I want the nursery to look nice, but I want to avoid the cutesy look. You know what I mean?