As others have said, you should certainly be sure that your test kits are reading in the ballpark correctly. My preference is for the Salifert NO3 kit. I cannot distinguish between 5 and 35 ppm of NO3 using the API kit. If you are using Seachem’s Nitrogen, half of that (as implied in the above posts) will not be read by an NO3 test kit. So, your nitrogen levels will be higher than the readings you get, if you dose Seachem’s Nitrogen. Additionally (I assume you have fish), your fish should be contributing NO3 and PO4, which could interfere with your estimate of how much N you actually have. Fortunately, in a low-tech tank, you don’t need much.
However, your issues may be more than nitrogen based. Plants need N,P, K and traces. You can measure P (PO4 API tests are good for this), but you can’t measure potassium and traces. Usually, in a low-tech tank, an average fish load will supply enough NO3 and PO4, leaving only K and traces to be dosed. For this reason, there are many K plus traces or K plus iron formulations. Your tap water probably has enough traces, so just adding the K (potassium) and iron may be all that you need. I suggest that you make sure you are dosing those while you check your NO3 and PO4 levels.
Additionally, since you are not injecting CO2, you will find that Seachem’s Excel will help considerably in adding a carbon source for your plants.
No: Purigen will not affect the NO3 that you dose. It could lower the NO3 generated by your fish, because it adsorbs the ammonia products in fish poop and plant rotting that eventually turn into NO3, but your doses won't be touched.