Sounds to me like you're right on track. It takes a long time for that nitrite spike to go away...you just have to be patient and/or find somewhere to get some bacteria seeded from.
Keep checking the ammonia and when you see it low add some more but don't add too much. Check the nitrite maybe every other day or every third day...you will see it almost disappear overnight. If you start seeing a lot of nitrate you know it is on its way down
If your nitrites and nitrates seem to both get stuck high, do a big water change, let things settle for at least a few hours and then check your levels and add ammonia if necessary. I'm guessing that maybe there is more ammonia in there than you think if you added very much to begin with...it is an easy test to misread. I wouldn't add any new ammonia unless you get a 0 reading (or pretty darn close to it). You just want to make sure that there is some ammonia in there every day either because it is there and measurable, or because you added some within 24 hours. This simulates having fish in there. Ideally it will start disappearing very quickly, but as long as you have enough bacteria to take care of a detectable amount of ammonia in the tank you should be fine.
You can help things along by making sure the temperature is nice and warm (around 80 is great), if you have some good oxygen content (ie lots of splashing from the filter output) and if you could find something to put some bacteria in there...like filter squeezings from a local store or a friend's tank.