Any time you have unproteced sex after stopping the birth control, you are at risk for pregnancy
. It is possible that the brown discharge and light bleeding is related to pregnancy. However, it is not likely, as most bleeding is not due to pregnancy, but more likely it is just a period, and it ,may take up to nine months after the depo shot for your periods to return to normal. If they don't become normal by then, you should see your doctor to figure out why your periods are not normal and to get treated for that problem.
I would recommend that you take a pregnancy test just to make sure. I hope this helps, please let me know if you need any more information.