celeste,
At this point you need to minimize the amount of toxins (ammonia and nitrIte from the fish waste) as much as possible. While it will be difficult to do, you need to severely cut down on feedings. I haven't seen it posted so how many fish do you have in the tank, what kind are they, and how big are they? This is very important so that we can judge exactly how much waste they are producing.
Since you are going to be cutting down on the food (I would feed a small amount every other day to start with making sure that ALL of the fish are getting a bite to eat) you do not need to vacuum the gravel. I would make sure that you did get all the waste and fish food up that is already there, but there should not be much more due to the lessened feeding. This is for their own good, and while they might not like you for it, it will keep them healthier.
Next are the PWC's. These are vital, but you need to get the values for ammonia, and nitrIte really low ASAP (under 0.5ppm ideally). I know you have the strips so they won't be very accurate but its better than nothing. Depending on the amount of fish I would try to do a 75-80% water change in one shot, give it an hour or so, then test. If either level is still off the chart or over 1ppm do another very large 75-80% water change. Make sure you are using tap water that has been treated with a dechlorinator, and make sure it is the SAME temp as that of the tank. The larger water changes you do the quicker the numbers will come down, and the less work you have to do.
Goodluck!
justin
EDIT: One last thing you can do if you have relatively good light in the tank is to pick up some live plants. For now don't worry about all the fertilizers and carbon dioxide additives, you need all the help you can get. Plants like hornwort, moneywort, anacharis, etc are excellent ammonia absorbers and should help to keep the levels lower between PWC's. You have a 55gallon tank, so it takes a LOT of waste (or in your case a month of no water changes in a new tank) to get the ammonia and nitrIte levels really high.
And I would recommend an air stone or two in your tank. While the oxygen level in the tank is probably acceptable, you need all the oxygen you can get with your fish. Since you have high nitrIte I'm assumming your ammonia level is probably not that bad in the tank. Therefore your main concern is the nitrIte. A little background on nitrIte: it acts like carbon monoxide to us, that is, it competes for the places where oxygen binds. What you get is essentially an asthmatic fish that cannot breath well (suffocating basically). The less oxygen in the water, the harder it is for the fish to breath. So I would reccommend an air stone or 2.