First off, welcome to Tropical Fish Keeping forum. Glad you joined us.
It would help to know your ammonia reading, and nitrate. As you probably now understand, nitrite is the second of the three stages in the nitrification cycle. And I would surmise that you are stuck in the second stage.
Frequent partial water changes with Prime is the best treatment. Live plants will certainly help, as they assimilate and take up a lot of ammonia/ammonium which means less nitrite and nitrate following. You might find some useful info here: http://www.tropicalfishkeeping.com/f...quarium-74891/
Also recognize that even with Prime, nitrite will still show in tests. Seachem themselves are not certain how Prime actually works with respect to nitrite and nitrate, but it usually detoxifies them by binding them somehow. But a nitrite test will still show "nitrite" at this "detoxified" stage. Prime is effective for 36-48 hours max, so if nitrite is still showing two days after using Prime, another water change with Prime should be carried out, and so on, until nitrite drops to zero. A 50% water change (half the tank volume) should be done at each change; presumably the parameters between tap and tank water are close (hardness, pH, temp) so this will not cause further problems.
Do not vacuum the substrate, as this might remove some bacteria. This is a debatable point, but I think it is still wise to leave the substrate alone. Just siphon out water and replace it with fresh treated with Prime. Double the recommended dose is usually suggested.
Obviously, do not add more fish until this is resolved, as that will only upset the balance more.