Conrad Hilton -- Checked Into Rehab After Mid-Flight Tirade

Paris Hilton's little brother got his ass into rehab almost immediately after he allegedly went nuts on a British Airways flight last summer ... TMZ has learned.

Conrad Hilton appeared in court Tuesday after surrendering to authorities investigating a bizarre incident. We broke the story ... 20-year-old Hilton allegedly berated and threatened the crew during the July, 2014 flight from London to LAX.

Conrad told feds he had taken a sleeping pill before boarding the plane ... which his attorney Robert Shapiro says could have caused the outburst.

Sources connected with the Hiltons tell us ... right after the incident ... Conrad voluntarily checked into a 30-day inpatient drug and alcohol treatment program.

Hilton was released on $100,000 bail at Tuesday's hearing. He was ordered to surrender his passport and remain in California.