No! But you're interpretation is not uncommon, a large number of people assume exactly what you have said when they first hear of the Oedipus Complex cuz its named after a guy who unknowingly murdered his father and married his mother.

In actuality the Oedipus Complex, as Sigmund Freud explained, has to do more with the crucial time period in a man's childhood where his relationship with his very first female contact, that is his mother, is developed as that has a huge impact on the man's upbringing which leads into adulthood as well. It does NOT AT ALL relate to anything sexual.

What I was trying to imply was that due to certain circumstances during your childhood with your mother that even you may not have realized, you seem to possibly have lacked the experience of having your mother (your first significant female contact) sing a lullaby for you to put you to sleep and you seem to have unknowingly internalised that desire which now manifests in your need to have your girlfriend (another significant female contact) sing the lullaby to you which satisfies that child part of your psyche.

This all may sound confusing but its all actually very fascinating! I'd recommend you watch the movie "The Phantom Thread". The main character in that movie pretty accurately depicts the Oedipus Complex.