I am afraid there is no direct connection between a fish being cheap in the shop and being easy to look after. All the low price of the neons reflects is that they are cheaply mass-produced in big fish farms in Singapore and elsewhere, not that this results in hardy fish that will be easy to look after. They are not in fact usually suitable for a new tank (though individual members have still had success with individual batches of strong fish). Black widows do have a reputation for being strong, but even they are going to have their stamina tested by their current circumstances.
Every fish, whatever its price, deserves to have its individual needs researched before purchase. I admit that shops often do not make you aware of this need, but fortunately there is a wealth of information on the internet these days.
Basically, you have added far too many fish to a new tank. If you cycle (=start up a new tank) with fish, you want something in the region of 1 inch of fish/5 gallons of water, that would be two black widows in your tank. After 4-6 weeks, once the ammonia and nitrites readings had returned to 0, you could then slowly have added more fish.
As it is, you are going to need to concentrate very hard on avoiding health damage to your current fish. Do as previous posters have advised, buy a liquid test kit and test every day for readings of ammonia and nitrites. Every time these go over 0.5 ppm, you need to do a partial water change of c. 20% (more if the reading is really high), replacing the water you take out with dechlorinated water. It will probably be some time before levels stabilise completely, and even then you are close to your full stocking levels.
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