I bought a cheap bike and a few days later I noticed the back wheel was slightly wobbly. I also hear a whooshing sound from the wheel rubbing against something but I can't locate where its coming from. I've turned the bike upside down and spun the wheel, I can hear it but there is no place where the wheel is actually touching something, its a real mystery. When I ride my bike I feel like I'm exerting a lot more energy than I should and the bike slows very quickly after I stop pedaling. What do you think the problem is, do you think it could be a result of the wobbly wheel alone?
I never learned to ride a bike. It is my deepest shame.
can you feel the bike wobblingas you ride, or just see it? If you can feel it then the cause is probably a damaged tire... if the wobble is all in the rim and spokes it is often very hard to feel even if it is easy to see. If it is the tire, the damage is often caused by a brake pad rubbing on the tire. Sometimes the tire will wear thru and blow out instantly and sometimes it will be ridable for some time before blowing. Either way you need to replace the tire and adjust your brake pads.
If you can not feel the wobble when riding but it is obvious when you look at it, then you likely have one or more broken spokes - usually this happens on the drive (chain) side after a new bike has been ridden a few hundred miles... and is usually the result of an improperly built wheel.
I bet that it's the bearing or axle issue. Wobbly wheel is when you do not spin it, but move it from side to side and it moves quite a bit - right? That means the axle could be broken, or bearings shot, or nuts on the axle that seat the bearing are not adjusted properly and the bearing move about on the cones. http://www.sheldonbrown.com/gloss_an-z.html#axle