Hi there!
Usually the cycling of the fish tank tanks anywhere from 6-8 weeks, and possibly longer with water changes. The spike in the Nitrite could possibly because you've added too many fish too fast... and on top of cycling the new tank.
The nitrites and amonia will peak and then fall.. with the establishment of the beneificial bacteria.
I would ease on adding any new fish into the tank until the cycling has been complete.. as it is unfair to the fish, because of the toxicity of nitrites, amonia. and are potentially lethal.. and nevermind the endless cost to replacing fish. I would recommend to keep up on the water changes, and make sure you are not overfeeding.. and just wait and be patience

I learned everything the hard way..
Here is the link to the 'sticky' about cycling the aquarium. That might help you out a little to explain the process a little clearer.
http://www.fishtankforums.com/5-fres...-aquarium.html
There are probably going to be more replies that are more informative.. than me.

Just trying to help with the knowledge that I know
Sarah