Just got depo-provera shot just finished my period a few days ago now getting brown discharge is that normal?

Yes: ~50% of women stop getting their period within their first yr on depo-provera; ~80% by yr two. However, many women will note irregular periods - fewer, shorter, lighter, more frequent, or even heavier, particularly within the first several months of use, including spotting (red, pink, brown). This is all normal. Call your dr if you develop persistent (8+days) and/or heavy (1pad/2hrs) bleeding.