I agree with Coursair. Before you get any more fish, make sure your tank is fully cycled - which means no ammonia, no nitrites, and nitrates below 40ppm. Neon tetras are particularly sensitive to water parameters, and are therefore susceptible to the high ammonia and/or nitirite levels in a new tank. If you don't have a test kit, get one. It's the only reliable way to know if your tank is cycled and ready for fish. I prefer the API Master Test Kit for freshwater. Seems a bit pricey at first, but considering you get more accurate readings than with dip-stick tests and you can perform the tests for a couple of years without running out of any of the solutions it is actually lower priced per test than the dip sticks.
Also, neon tetras are schooling fish and will do better with a school of at least 5 - 6 fish. You could house more than that in a 10g tank as long as you are careful with water parameters, but I wouldn't add more than that at once. Let your first 5 or 6 get acclimated, then add another 3-5 if you want to. I've found that neons are more active and hide less the bigger the school, even if the tank is "overstocked" according to the "1 inch of fish per gallon" guideline. I had 15 in a 14g tank, along with a couple of otocinclus, and they were just fine and more active than when I had fewer in the tank.