First your axle nuts . You will need to losen the outside nut first, so you can tighten the inside one.But first check and see if there is any play in you sprocket hud, it should be tight and not move from side to side.If it does tighten nuts.To check the bearings I would first spin the axle listen to see if I here any rough sound like griding noises or if whenn I tightened up the axle nuts it made it hard to spin the axle or it done something other than it should be doning ,I would pull the axle to look at them.Pulling the axle is not thst hard. Just take the rear tires off tthis will make the axle lighter,then remove the hub from the sprocket side of the axle,remove the axle nuts,slide the sproket hub off (before you do this you will need to remove the chain),then slide the axle out of carrier and inspect the bearings.If I go to the step of removing the axle I will have a set of bearings to replace the old ones with when I do it ,saves on down time of your shee
Good luck