It's hard to say for sure without a log but it's possible your PH fell, which caused the bacteria to lag a bit and then the nitrites spiked again. I wouldn't add fish until you can get this under control. You can keep dosing ammonia and testing the tank daily; if PH keeps dropping to below 7, you might need to add some crushed coral to the filter to try to keep it stable. You want to be able to zero out 4 ppms of ammonia in 24 hours and nitrites to stay at 0 consistently without water changes for at least a week before adding fish.
Also sorry if you mentioned this and I forgot but what's your PH out of the tap? ALso leave a glass of tap water out for 24 hours (stir it occasionally) and then test the PH again; sometimes PH can change after it gasses off and this will give us your "true" PH and what your tank's PH should be normally.