It could be possible that a psychologist prescribe homeopathic remedies?

Sometimes: There are some psychologists who have taken training in classical homeopathy. Depending on state laws, such psychologists may be able to give homeopathic remedies. States with healthcare freedom acts like mn and ca make it easiest. Extent of homeopathic training is most important for effectiveness though. Mental health disturbances are very deep, & you can't prescribe for these superficially.

They are not: Qualified to prescribe homeopathic medications. They may suggest that you consult with a homeopath, but unless they are trained they will not prescribe.

Prescriptive power: With the exception of Louisiana, New Mexico, Guam, and the military,psychologists do not have prescriptive power. You will need one of the following for that: a psychiatrist, a general practitioner, a nurse practitioner, or a physician's assistant to prescribe.