No, during the cycle your "good" bacteria is building up. It turns the Nitrites into (less toxic) Nitrates which shouldn't be a problem with regular water changes. Your ammonia/nitrites should not get high ever again.
You are doing great! You will know you're tank has cycled when the ammonia and nitrite are 0 and the nitrates go up. Test every week, or a couple of days after adding any new fish, and if the ammonia or nitrite go up do your water changes again until they come back down, also change 50% water if the nitrate gets up over 20. Best of luck with your tank.
I have one Chinease Algae Eater that I've put in his own 10 gal tank. He is REALLY agressive, and was ramming all my other fish. He is about 5" long, and from what I understand at this size and up they don't even eat algae much any more. I would flush him if I could :-\ Just can't make myself do it. :