The water you are seeing is almost certainly groundwater seeping under the foundation walls. Building another wall will do nothing to reduce the groundwater level. The best way to deal with the problem would be to reduce the groundwater level, which would require you to dig a drain line around the house. Typically, this is done using 4 inch perforated plastic pipe installed in a gravel filled trench, typically about 18 inches wide, and about 12 inches lower than the lowest part of the crawlspace you want to drain.
This only works if you can run the drain line out to a lower elevation, which could be a low part of your lot, the street, or a catch basin if the town allows it. If this is impossible, you can install a sump pump, which will pump the groundwater out under pressure, again hopefully to a low point. Sumps work fine as long as the power does not fail, but they are not as positive as a properly designed and installed gravity drain system.