SAN FRANCISCO, California (CNN) -- The mother accused of throwing her three young children into the cold waters of San Francisco Bay pleaded not guilty Friday to murder and assault charges.Lashaun Harris' public defender, Teresa Caffese, entered the not guilty plea on behalf of Harris, who kept her head bowed during the brief arraignment at San Francisco Superior Court.Harris was ordered held without bail, and her next court appearance was scheduled for next Friday. If convicted of the three counts of murder with special circumstances, she would be eligible for the death penalty. (Watch the latest on the case -- 1:48)Caffese told CNN in a phone interview that Harris is in a safety cell in a hospital facility and under a suicide watch."She's in shock right now," Caffese said. "I don't think it's really hit home yet." Caffese said her first priority is to make sure her client is OK. Harris, 23, has a history of mental health problems, including schizophrenia, her relatives said Thursday.A cousin said Harris was supposed to be taking prescription drugs for her treatment, but "she had quit taking her medication."Police arrested Harris on Wednesday after witnesses reported seeing Harris walk out to the end of Pier 7, which extends about 700 feet into the bay, and throw the children into the sea that evening. The body of 2 1/2-year-old Taronta Greely was found a few hours later two miles away from the pier.The bodies of the two other children, Treyshun Harris, 6, and Joshoa Greely, 16 months, have yet to be found, despite massive searches of the bay. (Full story)CNN's Rahul Bali, Rusty Dornin and Augie Martin contributed to this report.