sounds like neon tetra disease, it can cause a bent back, it can also wipe out all your neon tetras, take out all your infected fish, as the disease is spread when the healthy fish peck at the dying one! as far as i know there is no cure for this disease, so you might as well uthanise... although trying to nurse them back to health in a q-tank might have a snowball's chance...
for neon tetras, id just use a knife, decapitation is quick, and very easy to do on such a small fish