I've tried to answer this 3 times now and have ended up starting again each time.
You've got quite a number of concepts all jumbled up here.
Firstly subatomic particles themselves aren't in an infinite number of quantum states. In fact the whole concept of quantum mechanics is that such objects only have a limited number of states that they can occupy.
The Many Worlds Interpretation (and there are others such as the Copenhagen Interpretation) says that the universe splits whenever a quantum choice occurs which leads to an almost infinite (but not actually infinite) number of slightly different Universes.
You are not a quantum object - because of your size. You cannot suddenly disappear on one side of a wall and reappear on the other like an electron can.
We have no actual evidence for many worlds it's just a way of interpreting what we see. Stories of travelling between universes are really just stories I'm afraid.
There is a really good interactive site that goes through the physics behind some of this complete with Java applet experiments that are quite fun.
I strongly suggest you spend some time on it if you're really interested in this stuff:
http://www.colorado.edu/physics/2000/index.pl
personally I'd start with this bit:
http://www.colorado.edu/physics/2000/schroedin ger/index.html