Lamar Odom Snorting Cocaine at Brothel ... Popping Mystery Pills

Lamar Odom was snorting cocaine and popping mystery pills at Love Ranch before he fell into unconsciousness ... this according to police interviews with the prostitutes at the brothel.

TMZ Sports has obtained the search warrant police obtained to take blood from Odom at the Nevada hospital where he was receiving treatment.

According to the detective who signed the affidavit for the warrant, he interviewed the prostitutes who were with Lamar, who told him, "He possibly ingested cocaine in the bathroom adjoining in the bedroom." The detective said, "They indicated that they heard him snorting."

Police also interviewed Odom's personal assistant at the hospital, who said he knew Lamar and other celebrities did drugs. The assistant added he had actually witnessed Odom under the influence of narcotics.

As for the pills, investigators say witnesses saw Odom taking an "unknown substance in the form of an unidentified pill, which he obtained from his pocket in a plastic bag that was unmarked."

The pills were not identified -- but it seems unlikely they were the sexual enhancement pills Odom had taken since those came in a marked blister package that were sold at the Ranch.

The detective says in his affidavit they need a blood sample because Odom showed symptoms of an OD ... white substance coming from his mouth as well as bleeding from his nose.

As TMZ reported, our sources say doctors performed blood tests that revealed the presence of cocaine.

The police have not received the results back from the blood sample they took from Lamar, but the Sheriff has said if it shows the presence of cocaine, he could well be prosecuted.