It depends on the size of the backpack, the fullness of the flight, and the mood of the gate agents.
Generally speaking, a small kids backpack is a "personal item". A back pack like a kid would use as a book bag is a personal item, unless it is stuffed full, then it's generally going to be a carryon. A back pack that's really more of a woman's purse is going to generally be a personal item. A backpack like you'd go camping or hiking with is going to be a carryon, and might even be too big for that.
There 's really no reason to carry on everything. In your small carryon you should have a change of underwear, essential toiletries, a clean shirt, and perhaps a bathing suit or sweater. Also your laptop, camera, cell phone, etc. I can easily get all this into a carryon small enough to fit under the seat in front of me.
Anne