x2 on you have a cycle going on in this tank. Ammonia and nitrIte levels over 0.25 put fish in jeapordy- especially your rummynosed tetras. (IMO 10gal is really too small for rummynoses- they need much more room to swim)
NitrAte levels between 10-20ppm are a happy medium between enough to support plant growth but not toxic to most fish, so your nitrAtes are fine right now, but actually should continue to go up as the N-bacteria start to colonize your tank.
You fish are really at risk right now, and you need to do several things to try and help your fish through this toxic cycling process;
1-First you need to do a few PWC as soon as possible; enough to get those 2 levels down to 0.25. Try changing 25% twice, and see where that gets you? (multiple smaller PWC will be safer for your fish in this case)
2-Add more plants, especially some fast-growing floating plants would help(hygrophila/water wisteria, water sprite, hornwort, pellia- something along those lines)
3-If you know someone with a healthy established tank, see if they have some used filter media they could give you, and/or some mulm from the bottom of their tank. This will be full of the bacteria you need to break down the fish waste and keep the levels safe in your tank.
Good luck and keep us posted!