I was thinking that the current had to go though the transistor to be increased.
This highlights a dangerous misconception. Current is the flow of charge. Charge, like energy, is never created nor destroyed. Thus, you will never find a device where the total current flowing into the device is not equal to the total current flowing out. In more formal terms, this is called Kirchhoff's current law.
This makes sense. Is there any device you can put in a hose such that the water exiting is greater than the water entering? If so, it would be an infinite water machine. Likewise there is no infinite charge machine.
In your circuit, current enters through the base and collector, and exits through the emitter. The emitter current is exactly equal to the base current plus the collector current. Because of the transistor's gain, the base current is much smaller than the collector current by a factor of 100 or more -- this parameter is called \$h_{FE}\$ in the datasheet.
Because the emitter current is the sum of the base and collector current, and thus is also much larger than the base current, it's perfectly valid (and frequently useful) to attach things to the emitter of the transistor to make use of the transistor's gain. See Why would one drive LEDs with a common emitter?
Furthermore, your use of "before" and "after" suggests that you think you can start at the + terminal of the battery, then work your way to the - terminal following some linear cause-and-effect reasoning. You can't. It doesn't make sense, anyway. We call them circuits because they are just that:
cir·cuit (sûrkt)
n.
1.
a. A closed, usually circular line that goes around an object or area.
Current flows through the battery just like everything else. The electric charge moves in a circle. A circle doesn't have a start or an end, so you can't have a "before" or "after".
You don't need anything so complex as a transistor circuit to illustrate this; just an LED and a resistor will work. Try this:

simulate this circuit – Schematic created using CircuitLab
Is there any functional difference between these circuits? If you really want to get into the cause-and-effect chain, then you need to think at the speed of light, and read How does the current know how much to flow, before having seen the resistor?