We cross the border from Michigan into Canada all the time as we have a cottage in Canada. Searching CAN be random but often is done if there is something suspicious. What is visible when the border agent looks in your car windows (rolled down)? Sheets and school supplies? Or beer and a beer pong table?! Just be prepared to share appropriate info. “We are driving into Canada to drop off S at so-and-so college for the year.” I would recommend taking new stuff out of boxes/packaging - so there is no trouble with having to pay duty (not sure how they would deal with this for a dorm - but they ask us each time we cross if we have anything new will be leaving at the cottage). But if it’s out of original packaging they won’t really know new or used. They will ask how long “you” are planning to stay. They may ask about any fresh food (lunchmeat, meat, fruits/veggies) - this is more of an issue coming back into the states.
We have only had our car searched once in decades. We just had to pull over, get out of the car, fill out some forms and wait while they looked through things. We got a small hand slap for bringing back some deli lunchmeat. 