Okay, makes sense as you're asking about a BMX (my first guess: singlespeed of fixed-gear bike, with not-perfectly-round chainrings). I realize you don't know much about bikes, but that info (and what you explained in your second post) adds a lot to your question.
First, you could buy a new sprocket for your bike, or switch the sprocket from your brother's rear wheel onto yours. To do this you'd need a BMX freewheel remover, available at most bike shops. Probably 4-prong.
Here's the sort of thing.
With the rear wheel slipping, I suspect you've just not tightened the bolts on the axle hard enough. If you tighten these down correctly, there should be no slipping.
When the wheel does slip out of alignment, this could be connected to the apparent non-roundness of the chainwheel. But since you didn't have a problem with thise with your own wheel, perhaps the sprocket on the rear wheel is out of round. But then your brother should have had some problems with it when it was on his bike.
I don't see how a hammer treatment could get your chainring back into round if it's out of round.
My best guess is that your bottom bracket is loose, which allows play in the chainring's position. The Bottom Bracket is the bearings that the crank rotates on. If you take your crankarm (on either side), line it up with the seat-tube (or any other tube on the bike), and try to push it toward, then pull it away from the tube, and check for play. If there's play, your bottom bracket is loose. A lower-end BMX bike probably has a one-piece crank, and so you can adjust the bottom bracket by using an adjustable wrench to loosen the lockring on the non-chainring side of the bottom bracket, where the crankarm exits. Then tighten the cone (further inward along those threads), and re-tighten the lockring. You'll have to mess with this a few times to get it right, where the crank spins freely but without play.
Also, Sheldon Brown's article page is at
http://www.sheldonbrown.com/articles.html