To play 2NL full ring cash games ($2 100 big blind buyin, .01/.02 no limit holdem, 9-seated) you generally need about 20-25 buy ins to prevent from going bust due to bad luck. That means a starting roll of about $50 to protect you from swings.
It sounds to me like you may have an issue with tilt and loss chasing, meaning you move up in table stakes before you should to try to make up for a loss recently incurred. This is dangerous, and something you need to get a handle on. Even with proper bankroll knowledge, it is meaningless unless you have the discipline to adhere to it. You will need to set yourself some strict rules to follow proper bankroll management principles.
You won't be able to know if you are a winning player unless you strictly follow proper bank roll management. If you are able to be very disciplined, and you see your roll SLOWLY increasing over several months and tens of thousands of hands, you are probably beating the game. If, after tens of thousands of hands with strict bankroll management, you have slowly lost almost all your roll, you probably need to learn and practice a bit more to improve your game.
Regarding advice on bettering your actual poker game
skills -- try googling for some information on beating the micros. I don't have any specific advice on books for micro cash games, but perhaps someone else has a good one? There is a lot of information available on cardschat and other pokersites already, and you should be able to get started by reading some micro cash game guides.