I remember distinct scenes, but nothing comes up when I try general search engines. I watched it once when I was about 8 years old and was under the impression the name of the film was "Fear." But looking at that film now (released in 1996), it's not the one I'm thinking about at all.
The overview is a young girl (I can't remember, I think she was African-American) who has a telepathic connection with a murderer. He has constant access to her mind, but she has to try really hard just to get a glimpse of his. Upon some point in the story, she manages to see his license plate number and finds out he's at a laundromat. He gets away, and he's very mad and frustrated that she almost got him.
Another time, she heads to an airport to get away from him. He threatens her, and says if she doesn't get off the plane, he will kill someone. The screen shifts to him approaching her best friend in a dark parking lot, and he suffocates her with a piece of saran wrap.
I know she finds him in the end, and they have an intense physical fight. I am almost positive she kills him. But not knowing the name of this film is driving me absolutely nuts.