Anxiety and overthinking are treated by psychiatrist preferably as they are consider as functional(the mind ) disorder of your brain rather than any organic problem (lesion pertaining to your brain and nervous system), though they are highly interconnected. Usually anxiety and depression co exist together and one may be a secondary manisfistation of other vise versa. Proper evaluation based on history is needed for proper treatment. Thoughts pertaining to your problem can  have many factors generating them and proper evaluation and psychiatric interview is needed to come to any conclusion . And treatment is usually a mixture of pharmacotherapy and psychotherapy. Hope you find the information useful

Hi, I will answer in a few sentences. The difference between Psychiatry and neurology are Neurology deals with structural problems of the brain where as Psychiatry deals with functional problems of the brain. You see thoughts and emotions are functions of brain. Hence Anxiety and over thinking are Psychiatric issues. Anxiety, depression etc are emotions and emotions change the way you think/ perceive . Hope this answers your query .