Kathy and Rick Hilton visit Paris in jail on June 12
06/12/2007 AT 02:00 PM EDT
saw her parents through visiting-room glass Tuesday, telling them she has suffered cold and sleeplessness in jail but is just starting to get her appetite back, her mother said.
"It's tough in there. It's cold," Kathy Hilton said after she and Paris's father Rick had a 30-minute visit with their daughter Tuesday. "It's just good to see her."
This was the first time Hilton's parents have seen her in jail. Hilton told her mom and dad that she has finally started to eat, beginning with cereal Tuesday morning, Kathy Hilton said.
"She was very happy," Kathy said. "She wants to just do her time and get on with it."
In addition to losing her appetite, "She really hasn't had much sleep," said Kathy.
Hilton, meanwhile, faced problems outside of jail – she has been dropped by her talent agent, PEOPLE confirms.
"Paris is no longer a client," says Endeavor agency rep Michael Donkis, who declined to specify a reason for the move.
According to a source, Hilton was dropped last Friday – the day she was ordered back to jail
from home confinement. The move was announced in a company-wide email, the source says.
The Beverly Hills-based agency has represented Hilton since 2005, handling her deal for The Simple Life
Hilton spent her fourth night in a medical center at a downtown Los Angeles jail. She is serving out a 23-day minimum sentence for violating probation in an alcohol-related driving case.