Great question — answering as the UphillTech team:
This sounds like Charlie Bartlett . Let's look at the trailer... High school boy - Check Rich - Check Private to Public school - Check Wears uniform and not well liked - Check Psychiatrist - Check Giving counsel/drugs to fellow student in bathroom - Check I don't what else it could be!
Full answer by Skooba: https://movies.stackexchange.com/a/83392 (CC BY-SA 3.0).
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