Good thoughts and info so far, Some things to add that might help.
One indicator of OTS is the ph level. although not surefire 100%, one of the classic problems with OTS tanks is the PH drop that results from bio-acidification. The rapid water changes so commonly warned against will replace KH at too fast of a rate and harm the fish. If your tank Ph is noticeably different than your tap water PH (after setting out overnight in a bowl) then proceede very carefully as mentioned. my suggestion is 5-10 percent water change once or twice daily until the ph raises and stabilizes in a similar to tap range. The fact is if your tank water is different than your tap then you need to do frequent but very small water changes to slowly acclimate your fish to the changing levels. the blanket warning that you should not do major water changes is only half correct and is far too often thrown around without any explanation. the faster you can correct the situation the better off you are, but you need to protect your fish while working on the problem.
If every parrameter of your tap and tank are similar except of course the nitrate level then large volume frequent water changes are your best defense. There is no danger to the fish because the water you put in is not a lot different than what you take out. Some simple testing will help you to know what is the best course of action. reduction in nitrates won't shock your fish. rapid changes in ph and TDS (total dissolved solids) levels will shock your fish.
We can all guess from a distance that you do or don't have OTS, but you can do some testing and know for sure.
Nitrate on it's own is not highly toxic ( but is toxic to some extent) however a tank with high nitrates indicates a tank with high pollutants and usually high TDS. many of which we cannot test for. The nitrate is our indicator, not the only concern. Most of the recent studies I've seen on nitrate toxitity simply don't account for other pollutant build-up in the tank. This is also why simply adding a bunch of plants will not prevent water changing needs forever in a typically stocked and fed tank.
AP test kits are decent( not the best in the world, but generally good enough for the hobbyist), I use them as well. the Nitrate test kit in particular is a little difficult to use, but it always reads low when it is wrong IME. with this in mind, I would guess you have a problem to deal with even if the kit is off. the easy test is to take a sample to the LFS and see if they get the same numbers your test gives you. better safe than sorry especially when the LFS's will verify it for free.
Lastly, 2 months seems like a short time to develope OTS, or even nitrates as high as you report. the most common cause of nitrate buildup is overfeeding. after you get through all of this, you may want to re-evaluate feeding levels for your fish. Very few hobbyists are good about not overfeeding. I know I feed way too much, and I feed far less than most people.
dave