The best way to get Nitrites down is to do water changes and not feed the fish near as much. Your ammonia spiked because that is the first stage of the cycle. Any chemical for the nitrites will just make them go down for a certain time. One or two water changes isnt going to make them drop really fast. I did multiple water changes, one every 5-6 hours, when mine was cycling and that helped. Make sure you add the right stuff to get the tap water safe for the fish. It takes time, as the cycle must run. Soon those Nitrites will turn into Nitrates. After that, the nitrates should gradually go down and the tank will be done cycling. Keep an eye on the fish for signs of stress, like gasping at the top for air or not swimming as much. Also, if you are adding chemicals, make sure they dont harm the fish in there now, as some chemicals hurt certain fish.