I have a lot of mental problems, should I see psychologist or psychiatrist?

You can start with . Either. Usually both psychiatrists and psychologists can do comprehensive diagnostic exams. The psychologist may refer you to a psychiatrist if you need psychotropic medications ; the psychiatrist could refer you to a psychologist for talking therapy.
Any one of them. Any one of them will be a good start.
The main reason. To see a psychiatrist 1st would be if medication was going to be needed. If someone is severely depressed and suicidal or if someone is hallucinating of out of touch with reality, medication may be necessary right away. Psychotherapy with a psychologist would also be needed if the psychiatrist only manages medication. .