Take the wheel out and pull the qr skewer out. If you can pull the axle out as well, you have a broken axle, If you can wobble it without it pulling out you have one of a few things (loose cones/knackered bearings/broken bearing cups/mixture of the previous). The other thing it could be is a bent axle, you can see this by spinning the axle and seeing if the end raises and fallls with eath rotation. From what you said it sounds like the cones need tightening, but not sure what grub screw you are on about, what hub do you have?