Like others, I'm assuming the bike has a quick release. I'd start by checking the brakes since you said you have not checked/adjusted them since last fall. My guess is that is the reason for the rubbing, especially if you have a thru-axle hub. Because.....
I take the front wheel (thru-axle) off and on my disc brake bikes all the time and the pads never rub. The thru-axle keeps everything aligned, unless something gets knocked while you put it in and out of the trunk.
A bike carrier is a good idea since you're transporting the bike every day, A good investment for the use you'll get from it. But make sure it's one you can lock in place so it doesn't get stolen. It would be a big hassle to have to remove it, stash it in the car, and replace it every day.
Last edited by Camilo; 05-09-22 at 11:44 PM.