Yes. Fluoxetine can cause insomnia, Diazepam is prescribed to counteract this, however its effects are reduced when taken on a regular basis. Once your body chemistry is settled there should be no need for ‘sleepers’ except in extreme circumstances. If insomnia persists and the Diazepam is not effective enough you should speak to your GP.
As with all prescribed meds steer well away from alcohol and other recreational drugs.