"Grow" by itself is much more broad, but really only talks about something getting bigger. Although it can also be used to describe things like skills and talents becoming better rather than just physical size. "Grow up" is the term we use when speaking of other people, as it can refer to aging (He has grown up ; My child is all grown up) or gaining maturity (He needs to grow up). Although I can't really say either of your sentences are ideal. If I were to express a positive when referring to a child getting older, I would say "My child has grown into a lovely (or any descriptor) person."

Hello, You use "grow" when you describe something growing, for example hair or a plant. The sentence would be "My child has grown up lovely" because the phrase "grow up" describes someone (child, kid,..) growing up and getting older. I hope I helped.