''AT xyz school'' is indeed correct (vs. ''from'').  However, "I have done my schooling'' is very awkward and would not be used by a native speaker.  If this is just in conversation (not for your CV), then a simpler form would be better: ''I studied at XYZ school''.  ''I went to school/university at xyz.''  British English may differ, but in US English I've only heard ''schooling'' used in formal writing. 

That was some harsh schooling by Emily. 

"I have done my schooling at xyz school" is more correct.