Add the sandwich cookies to the bowl of a food processor and pulse just until roughly chopped. Add the cream cheese and continue pulsing until the mixture is smooth and there are no large visible pieces of cookie.
Line a baking sheet with parchment paper. Using your hands, pinch off pieces of the mixture and roll it into 1-inch balls. Arrange the balls on the baking sheet then insert a lollipop stick into each and freeze them for 20 minutes.
Once the cookie pops have hardened, melt the red, white and blue candy melts in separate bowls according to package instructions. Dip the chilled cookie pops into each of the candy melt colors, shaking off any excess, and then immediately top them with the corresponding red, white or blue sprinkles.
Return the cookie pops to the baking sheet. Refrigerate them an additional 5 minutes until the candy melt has fully hardened then serve. (See Kelly's Note.)