After my period, or on the last day rather, the blood becomes brown discharge. How long does the brown discharge last and/or can I stop it myself?

Brown. Its likely just old blood coming out, which is relatively common. However, if you're sexually active and this has an odor it could also be an infection. If that's the case then I would see a physician (family or gyn) on a day you note the discharge especially. Also a good time to maybe start a birth control pill and shorten your period.