About a week before a 3-week tour, I would put new tires on the bicycle. Leave your old tires as spares in case you need them some time after you get back

If you're concerned about mechanical wear, take the bicycle into the shop for a quick tune-up. And ask your shop about the brakes.

Do you have time to take a class? It's not a bad idea to take an intro bicycle maintenance course, especially one that emphasizes on-road repairs. Your shop might have something like that, or maybe the local cycle-touring club.