They look healthy to me but before you worry about any possibility of disease, your first priority is to get your tank cycled and stablized. Ammonia is toxic to fish even in small amounts. NitrIte even worse than ammonia.
If you haven't already I would get a api master test kit and watch your ammonia levels and nitrIte levels closely. Do partial water changes like 25% or so every few days to keep ammonia down and you should look into two products called seachem prime and stability. The prime will detoxify the ammonia so it won't impact your fish as much (add it in with your water changes and follow dosing on bottle, it's easy) and stability is a bacteria kickstarter that will help establish your good bacteria (same easy dosing). If you start seeing nitrAtes then your tank is cycling properly. Once all the cycling is taken care of (meaning all ammonia and nitrItes are being converted to nitrAte) and they still look like they may be unhealthy, then you should revisit the possibility of disease.
For now I would hold off on buying any new fish and get what you have situated. I've owned neon tetras for years and they are amazing schooling fish so I can understand the appeal
good luck and if you have any questions everyone on this forum loves to help!