I think I might have depression, should I go to a psychologist or a psychiatrist?

Severity. Get a psychiatric evaluation to determine severity of symptoms of depression. Medications may be warranted. Also find a reputable psychotherapist to help you figure out what depression means to you, and how to better deal with it. Optimally medication and therapy together works best.
Either should be . Able to accurately diagnose your condition. The psychologist can provide talking therapy and may refer to a psychiatrist who can rule out underlying medical condition and prescribe indicated psychotropic medications. Or you could start with a psychiatrist who may refer you to a psychologist for therapy.