Just for review, the nitrate *should* show up after the nitrites spike. Assuming your tank water was nitrate-free to start with, you'll need the ammonia to turn to nitrites, and then the nitrites turn to nitrates before you really see any measurable nitrates.
Are you using tap water? Have you tested the source water you're using for nitrates? If you started with nitrates, you'll always have those nitrates until you do a water change.
In short... there really isn't a nitrate "spike". Whatever nitrates you end up with after your ammonia and nitrites have gone to zero will be what you have until you do a water change. Water changes are normally how nitrates are reduced.
Oh... and cleaning the glass didn't mess anything up. You're fine there.