if your car is pulling when u stop it should be your brake system warn pad, warped rotor or calaper piston is sticking. if you open your hood and just grab the base of the fan u can pull on it up or down and it shouldnt move up or down should only spin, now after u say it pulls when u stop i belive its going to be your brakes its more of a wear part than your fan. if the car pulls to the side while ur driving to i would check the alignment and tire pressure.
if your tires arent balanced or the weight came off it can and will give u a tire wobble while u drive, it can be unnoticeable at lower speeds. its hard to say without listening to it or driving it but u now have some ideas on what it probably is(brakes) a dealership will charge alot more than a shop though just some food for thought norm there like 85+hr shop rate thats why i always go to a garage shop. hope it helps