REHOVOT, Israel (AP) _ Ida Nudel, the ''Guardian Angel'' of Soviet Jewish dissidents who fought and finally won a 16-year battle to emigrate, says the transformation from outcast to celebrity has left her despondent and ill at ease.

Instead of enjoying freedom, Ms. Nudel is fighting depression and exhaustion as she wrestles with the demands and uncertainties of her new life in Israel.

''In a single moment, I arrived on another planet, in an absolutely different civilization and life,'' the graying, 4-foot-11 Ms. Nudel told The Associated Press last week in her first in-depth interview since leaving the Soviet Union on Oct. 15.

''When I was left alone in my sister's apartment for a few hours, I couldn't figure out how to turn on the faucet,'' she said. ''For someone like me, this is very depressing.''

''Also, in the Soviet Union, I was accustomed to living among a hostile population. Here, the attention is too strong for me to cope with,'' she said, clutching her shirt collar close to her neck and stroking the collie that was once her only companion.

Ms. Nudel, 56, was first denied permission to emigrate in 1971 on grounds that she might have overheard state secrets while working as a bookkeeper for the Moscow Institute of Hydrology and Microbiological Synthesis.

Eventually fired from her job as an accountant and separated from her family, who had been allowed to come to Israel, Ms. Nudel channeled her energy into working on behalf of imprisoned Jews in the Soviet Union. Her tireless efforts won her the nickname of the ''Guardian Angel.''

In 1979, Ms. Nudel was sentenced to four years in Siberian exile for her activism. In 1983, Soviet authorities refused to allow her to return to her Moscow home, and she was forced to live in isolation in the southwest corner of the Soviet Union before emigrating.

Today, she lives in a government-provided apartment in a high-rise on a busy shopping avenue in Rehovot, 15 miles south of Tel Aviv. Instead of being shadowed by the KGB, she is mobbed by well-wishers on the street.

The woman who was without a telephone for the last eight years now receives more than 20 calls and 50 letters a day from around the world, some notes addressed simply to: ''Ida Nudel, new immigrant.''

She is inundated with requests for public appearances and has little private time.

''I never imagined people would be so carried away,'' said Ms. Nudel. ''I was in a shop the other day when the owner recognized me and got goose bumps. He was excited because he had been hearing about me since he was a child.''

''But put yourself in my place,'' Ms. Nudel explained agitatedly. ''When someone just looks at you and says they have goose bumps, it seems abnormal. The reaction is too strong for me to cope with.''

Soviet Jewish activist Natan Sharansky, freed in a prisoner exchange in February 1986, has coped with fame by hiring a public relations spokesman who filters his telephone calls and contacts.

But Ms. Nudel said she doesn't want to remain a public figure like Sharansky. She wants to begin a normal, private life.

She is, however, going with Sharansky and other Soviet Jewish activists to the United States during the Dec. 7-10 summit between President Reagan and Soviet leader Mikhail S. Gorbachev. The activists plan to demand that the United States raise the issue of Soviet Jews during the meeting.

Ms. Nudel, who never married, relies heavily on her younger sister, Elena Fridman, for support. But the sisters, separated for 16 years, have had little time together lately.

''By the time we are alone together, we are too tired to talk,'' said Mrs. Fridman.

They have found one another altered.

''Elana has new self-assurance. She can insist on things. She is a completely different person,'' Ms. Nudel said.

''We have both changed,'' said her sister. ''We had a hard way to go for 16 years. Ida's hair is grayer, she is older. I wasn't quite prepared for it, because how she was going to look was the last thing I thought about.''

While Ms. Nudel hates the adultation heaped upon her, Mrs. Fridman sees it as a sign of work done well. G ''For 16 years, I sought to keep Ida before the public, so they wouldn't forget,'' said Mrs. Fridman. ''I like it when people recognize Ida on the street and are excited to see her. I feel joy because it is something that came out of my work.''