The rapper's ex, who works as a model, makes the shocking claims in her request for a restraining order against him ... telling the judge he's been threatening her ever since she broke things off with him.

According to the docs, obtained by TMZ, the gf claims Shy has repeatedly told her he will kill her and her mother. She says he's been making the threats ever since she broke up with him in April ... and she says he sent her a text message that said, "Ima f*** ya life up."

Shy's ex claims she started dating Shy in December but broke up with him on April 28 because she says he has "anger issues." She says Shy did not take the breakup well and things reached a head on May 13, when he was arrested for allegedly threatening her.

In the docs, the ex claims on May 13 she was driving around Los Angeles and noticed Shy was following her. She says she was stopped at a red light when he got out of his car and approached her car, banging her car with the handle of a gun. She says she drove away but he followed her and tried to run her off the road, hitting her car with his car and causing damage.

TMZ broke the story ... Shy Glizzy was arrested on May 13 on a felony charge of making criminal threats after his ex told police he pulled a gun on her.

The ex claims she's told Shy to stop contacting her, but she says he keeps messaging her, threatening to kill her, and post explicit pictures and videos of her without her consent in what she believes is an attempt to ruin her modeling career.

Shy Glizzy's ex also claims he texted her best friend, "Imma get her a** beat."

The judge granted a temporary restraining order ... and now Shy Glizzy has to stay 100 yards away from his ex and he's barred from contacting her. The judge also prohibited Shy from posting or distributing any explicit photos or videos he may have of the two.