When Alice Lowery first applied for public housing she was homeless and pregnant with her youngest son. That son will be 13 in January and Lowery is still on the city's public housing waiting list.

After stints of living with her family and with friends, she now lives with a 15-year-old son in a small rented room. The 13-year-old son lives with his father in Southeast because there is no room for him.

A 17-year-old daughter who suffers from depression and a nervous disorder left the cramped room and now lives with her godmother, and her 15-year-old son Malcolm also wants to move out and stay with another relative, because of the living conditions.

"People don't understand what it means not to have your own house," said Lowery, nervously twitching and fidgeting as she talked. "It's like being stuck in quicksand. You can't do anything else right. You keep sinking."

The city's waiting list for public housing has grown to 13,000 families, mostly single mothers with children, and a large majority have been on the list for several years.

Meanwhile, one-sixth of the District's public housing units sit vacant and in disrepair, primarily because the city government has not spent nearly $9 million earmarked for their renovation.

The city government is asking for an extension from the federal government, which has told local governments to spend the money by the end of the year or lose it.

While the bureaucratic wars go on, people like Lowery, 33, quietly wait for a place to call home.

Ironically, Lowery rents a room from a family that lives in a Northeast public housing project. She pays the family $100 a month for a 12-by-12-foot room, packed wall to wall with her life's belongings. She and her son are forced to share a sofa bed.

Eight other people live in the four-bedroom unit.

In July, doctors at Children's Hospital, where her daughter was admitted for her nervous disorder, wrote Lowery that a more stable living arrangement might aid in her daughter's recovery. Because of her daughter's illness, Lowery already had applied to the city a second time for emergency housing. The request was denied.

"My daughter was in the hospital and I wanted to bring her home," she said, sitting in the one chair in her room and speaking in a trembling voice. "The doctor said she shouldn't come back here, that I should get another place.

"When I got that letter saying my request was denied I was real down. I feel stuck in this place."

One of the daughter's doctors, who asked not to be identified, said that getting the family back together would make it easier for Lowery and her children to discuss their problems and get joint counseling that would help stabilize the family.

"I miss my poor children so much, but I try not to think about it," said Lowery, who quit her job as an office cleaner a year ago after her daughter got sick.

On Wednesday she filed an appeal with the city's housing department, which operates 11,500 public housing units, asking for reconsideration of her most recent application for emergency housing.

A housing department spokesman said Lowery had failed to keep her first application active and reapplied for housing in 1980. But the spokesman said the office has such a backlog that it currently is working to fill requests filed in 1977.

Lowery first applied for public housing in 1972, said Vivian Tapscott, who is in charge of the public housing waiting list.

But in 1978 Lowery was removed from the waiting list after she failed to answer a letter sent to her by the housing department asking if she still needed housing, Tapscott said. Lowery claims that the mail was sent to the wrong address, a common complaint of applicants dropped from the list.

If Lowery is approved for emergency housing, Tapscott said, she probably would be at the top of a list of 65 people waiting for two-bedroom apartments, because her application was made in 1980.

"We are working on 1983 emergency applications now," Tapscott said.

There is no waiting list for emergency cases needing one-bedroom units, but there are 90 to 100 families waiting for three-bedroom apartments, Tapscott said. Most of the city's public housing units are efficiencies and one-bedroom apartments.

Who gets approved for emergency housing is determined by a point system, Tapscott said. Applicants receive points based on their income, how much they pay for housing, crowding and whether the family's home was burned or condemned. A housing department letter to Lowery said that "of the necessary minimum of 25 points, your rating is 13."

She received two points for paying $1,200 a year in rent, six points for income (she receives $327 a month in public assistance) and five points for crowding.

"They didn't say anything about my daughter being sick," she said. "That doesn't even matter."

If Lowery had received at least 18 points, then factors such her daughter's illness could be considered, said Tapscott.

According to medical forms from Children's Hospital, Lowery's daughter, who did not want to be identified, suffers from "depression, panic attacks and mood disorders."

Once, Lowery said, the family had "a nice place," a three-bedroom home that she rented. When times got tough, she moved back to her parents' house, hoping to save money to rent another house.

But then her mother died. Lowery sees that death as the beginning of her downward slide. Her father sold the family's home, without offering it to any of his children, and moved in with another woman, she said. For the first time in her life, Lowery had no home.

Lowery said that once she tried to kill herself.

"I wouldn't do it again," she said. "I decided living was better. I'll go through anything for my kids. If it was just me in this life, I'd been gone."

A house, Lowery believes, would end the family's separations and its tense living conditions.

"I think everything would change," she said. "We could all live together. I could leave my kids at home and go look for a job, with peace of mind."