Is it possible to make a ±3.3 power supply from 9V battery?
Depending on how much current you need, and how well balanced the load is there are several solutions.  

The easiest to implement is probably using TI's TLE2426 'rail splitter' which will give you a +/- and a virtual ground. If the output current from this is insufficient it can be buffered with something such as a BUF634 (eye wateringly expensive) or a discrete stage.