And there's the source of the nitrates....
The longer you use tap water, the worse time you'll have getting the tank to a good healthy spot. If you cannot find someone to buy some RO/DI water off of (including other members), you'll probably need to make yourself a deep sandbed in the sump (or a remote deep sandbed in a 5g bucket). That will help act as a nitrate sink. I wouldn't do anything to increase your bioload (buy more fish/feed more).
Speaking from personal experience... When I started this hobby, I couldn't afford it, but I didn't realize what I was jumping into. the more I bought, the more I had to buy to fix more problems. When tap water caused my tank to be nothing but green hair alage, we resorted to just purifying water through a Brita filter. Yeah, no joke. It wasn't much better, but it was better than tap water! It was cheap on the short term, but would be terribly expensive in the long run. Some people buy gallons of (distilled, I think) water from the grocery store.
I'd also skim wet if I were you.