My rear bike wheel is wobbling back and forth when I ride. Nothing that I have done has worked and I was told that it was gonna cost $100 or more to fix. what do I do to fix it properly?
If it's wobbling side to side, there are two problems that are possible; Your cup-and-cone bearings could be loose or your wheel could be out of true (slightly buckled.) Take your wheel off and hold the axle. Wobble it up and down a few times. There should be absolutely no movement besides the spinning it's meant to be doing. If this is wobbling, just tighten the hub cones slightly until there is no play. The rule is No play, No binding. This means having it borderline between perfect no play and perfect no sticking, otherwise it'll make your ride unpleasantly harder.
If it's wobbling at 0' and 180' points of the wheels to make it slightly oval, that is also to do with wheel being untrue and buckled, or trued incorrectly. This job is a totally different ballgame. This usually happens when the spokes have been tightened more on one side than the other, and is a pain to fix, even for me, after repairing bikes for over three years now.
Worst case scenario, you could be looking at missing spokes or a bent axle. Maybe even some trashed bearings, but are usually rather cheap. A good thing to do if you're wanting to learn to do hubs is look at RJTheBikeGuy on YouTube or Global Cycling Network on YouTube. Both are extremely helpful with their guides.
I really, really apologise if this doesn't help, and I hope you get back to riding again!
Discovered that my wobbly rear mtb wheel was caused by the screws holding my drop outs into the frame were loose on both sides. Once tightened up, no more wobble and precise gear changes again! Have also had a wobbly rear tyre on a true rim from not properly engaging the tyre bead to the rim. Easy fix is to pump the tyre up to 40 psi and wait for the "ping" sounds as the tyre snaps into place on the rim bead.