Could you power a complete circuit using a Dc-Dc boost inverting IC?
how can i have a common Ground point with my 3.8V power supply?


A cheap (but low-power) solution is to use a buck converter in an inverting buck-boost configuration.



You can also find chips specifically designed for inverting buck-boost topology. 

Or isolated converters (forward, flyback, ...) that allow the output ground to be connected arbitrarily relative to the input ground (including connecting the output positive terminal to the input negative terminal).

If you are strictly bound to use a certain regulator IC designed for boost operation, you can probably use it to build a flyback inverter:



(image source and more information)

With this isolated design you can make a negative output by simply swapping the Vout and output ground connections.


  if i use a POWER mosfet to control another circuit (led array for example), the voltage i send to the Gate of the Mosfet, cannot activate it.


Another option, rather than changing your power supply circuit, is use optocouplers or relays to connect control signals from one ground domain to the other.