Hello, Nurse!

A male character pretends to be sick or mentally ill just to get close to an attractive female medical professional.

The Many Loves of Dobie Gillis

Appearances

• The Many Loves of Dobie Gillis: Season 1, episode 35, "The Unregistered Nurse" (1960). Dobie falls in love with a nurse, but she's not interested in him, so Dobie decides to play on her sympathy to win her over. He looks up an illness that he thinks he can convincingly emulate and goes to the doctor's office, but the disease turns out to be much more serious than he thought.
• The Odd Couple: Season 1, episode 16, "Lovers Don't Make House Calls" (1971). Felix is sick, and his usual doctor isn't available, so an attractive female doctor substitutes for him, and Oscar falls for her right away. He wants to ask her out, but he can't get in touch with her, so he pretends to be sick and makes an appointment with her.
• Cheers: Season 7, episode 18, "What's Up, Doc?" (1989). A beautiful psychiatrist friend of Frasier and Lilith visits the bar, and Sam is immediately smitten with her, but she won't give him the time of day, so he makes an appointment with her and pretends he's impotent.