Conrad Murray's Lawyers -- FIGHT During Jail Visit

Conrad Murray went from star prisoner to star witness at the L.A. County Jail today ... when a FIGHT broke out between his lawyers during a jailhouse visit ... TMZ has learned.

Sources close to Murray tell us ... Murray had been complaining about pain in his right arm and shoulder for the past couple of days ... and today, two of his attorneys (who are each working on different cases) raced down to the jail to check in on The Doc.

The first to arrive was J. Michael Flanagan -- who reps Murray in all matters relating to the Michael Jackson manslaughter case. JMF arrived with his 30-year-old son Ryan, who's also a lawyer but isn't working on the Murray case.

After the Flanagans began to visit with Murray in the jail, Murray's other attorney, Valerie Wass, showed up. Wass reps Murray in all matters relating to the California Medical Board and the appeal of his criminal conviction.

According to our sources, Wass claims she tried to enter the visitation room to speak to Murray, but was physically blocked -- and pushed -- by Ryan. Wass claims Ryan and his dad proceeded to shout at her until they left.

We're told Valerie eventually got to meet with Murray --and immediately afterward, she filed a battery report against Ryan.

As for The Doc, one source tells us Murray witnessed the whole thing -- and if there's an investigation, he could play a key role in the case.