. I went downstairs to the basement and just randomly turned off and on all valves I see going into this bathroom (which was right above me in the first floor).
Describe how you think the pipe are run. Describe how you bath is laid out.
No respectful plumber would run pipe in an exterior wall unless there is just no other way. Pipes in and interior wall do not freeze as long as there is heat in the house.
If you see the pipes in the basement you can probably figure out how they are run. Of course by that I mean are they in an interior wall or and exterior wall. To a first floor bath they certainly should be in an interior wall.
Describe how this bath is laid out. By that I mean, what is on an exterior wall and what is on an interior wall. I am guessing that your sink and vanity are on and exterior wall and so is the shower valve for the shower.
Usual piping would be to go up from the basement to the bath at the sink with both hot and cold. From there the cold would branch to the toilet in one direction.
The hot and cold would branch in the other direction to the shower.
I guessing that you pipes go up in an exterior wall to the sink and then go through the exterior wall to the shower. Any pipe in an exterior wall is subject to freezing. The most likely place to freeze is in the wall behind the cabinet or vanity. That is because the cabinet prevents heat in the house from reaching the wall. Therefore, you will want to open cabinet doors and add extra heat during extreme weather conditions.