Your plants are probably saving you (and the fish, more to the point). Amazon swords are fairly rapid growing plants, and yours look in good shape. You might be amazed at how much ammonia/ammonium these can take up as their preferred source of nitrogen. And when plants use the ammonia, nitrite is not a by-product, and that means no nitrate as well. Though some ammonia will get past the plants to the nitrifying bacteria, but (hopefully) not enough to cause issues.
Floating plants would really seal the deal, and they would calm the fish a lot. Angelfish come from very dim waters and do not like overhead lighting, so floating plants help reduce this, and that makes them less timid to other things as well--like the kids!
Monitor ammonia for a few days though, just in case. But given the volume, and the small size of the fish, the plants are likely easily handling this.
BTW, swords being heavy feeders really benefit wiith substrate tab fertilizer, if you don't already have this. Seachem's Flourish Tabs are one of the best.
Now, to something really important...you must do a weekly partial water change regardless of test results. Change at least half the tank volume, but 60-70% is better. Once each week, forever. nothing is as important to fish health.