Dragging her bum over the carpet sounds like worms. Regarding that she is an outside kitty I would give some de-worming pills.

Whatever you described does not sound like an UTI. An UTI starts with a kitty peeing outside the litterbox or with a kitty who goes to the litterbox every ten minutes and not peeing or only a little peeing.

You should be able to tell the difference whether she is straining to pee or to poop as the body shape is different.