Sometimes yes, and sometimes no, depending upon additional facts.
First of all, we don't know what kind of statements were made to John Doe's psychologist. In the question you state:
I say negative stuff about John Doe to my psychologist, stuff which
isn't defamation per se.
Negative stuff about John Doe is a defamatory statement in an older, traditional sense of the word in a legal context, but isn't necessarily a defamatory statement under modern legal standards. The modern U.S. law of defamation is summarized here, and is relatively uniform in the U.S. because it derives from a shared heritage of common law tort law and because it is limited by a shared body of U.S. constitutional law interpreting the First Amendment.
We know that the statement can't be one of the following four matters:
Indications that a person was involved in criminal activity
Indications that a person had a "loathsome," contagious or infectious disease
Indications that a person was unchaste or engaged in sexual misconduct
Indications that a person was involved in behavior incompatible with the proper conduct of his business, trade or profession
These statements cannot be defamatory under U.S. law, for example, if they are true, or if they are statements of opinion that do not unequivocally imply statements of fact that are not true.
We also need to know what information the psychologist shared and why.
The psychologist is only authorized to disclose confidential information about John Doe's mental health to third-parties if it is particular kinds of information (e.g. he is a threat to himself or a threat to others). The strict legal privilege against disclosing such information in court, even pursuant to a subpoena, is typically limited to confidential communications from the patient/client himself (often modeled on the attorney-client privilege), but the expectation of non-disclosure is typically broader, not as a function of a legal privilege, but as a function of a psychologist's broader fiduciary duties to the patient/client.
If it was not that kind of information, it might not be foreseeable that your statement to about John Doe to the psychologist would cause harm and harm is not presumed if the statement is not defamation per se, so the chain of causation between your statement to the psychologist and the harm.
Also, while the New York Times v. Sullivan, actual malice test, which makes statements actionable only if they are knowingly false or made with reckless disregard to their truth or falsity only applies to public figures and matters of public concern, almost anything that a psychologist for John Doe could legally share would almost by definition be a matter of public concern.
So, either the psychologist breached a duty of confidentiality, in which case the chain of damages caused by the statement is broken, or the statement to the psychologist was a matter of public concern, in which case it is only actionable if you knew it was false, or if you said it with reckless disregard for the truth. (There might be valid grounds to sue the psychologist for a breached duty of confidentiality even if the statement was not defamatory in the usual U.S. sense because was actually true.)
On the other hand, the psychologist might have felt at liberty to disclose the information if he was led to believe that it was not confidential mental health information, either because the psychologists believes that the information is widely known to the general public, or because the psychologist believes that the information is completely unrelated to his mental health.
For example, if John Doe is the Mayor of the local town, disclosing that John Doe is the Mayor would not be a confidential fact. Similarly, if John Doe is the tallest man in town at 6'10", disclosing his height would probably not be considered a mental health matter that a psychologist had a special duty to keep secret.
Now, if you did indeed knowingly make a blatantly false statement to John Doe's psychologist that was something that the psychologist had a right and duty to disclose and that caused John Doe quantifiable economic harm, this probably would be actionable defamation.
But, it is hard to come up with examples of something you could have said to John Doe's psychologist that would not violated expectations of confidentiality, while not constituting defamation per se. Certainly, this involves a fairly small subset of the fact patterns that could be present in the question.
But, I suppose that there could be statements like that.
For example, suppose that you knowing lied when you told the psychologist that you saw a photo on John Doe's Facebook page of John Doe legally killing defenseless bear cubs while they were hibernating. This is something that causes many people to think ill of a person, but isn't a crime, isn't a disease, doesn't involve having sex or infidelity, and may very well have nothing directly to do with John Doe's business in any direct way, so it isn't negligence per se, but it could cause people to cease to do business with him. And, the psychologist could plausibly think that since this was not a confidential statement about John Doe's mental health that he was legally required to keep secret because according to you, John Doe has already posted this fact publicly for all of the world to see.
In that scenario, you probably would have defamation liability to John Doe for the amount of economic harm that he could prove was caused by this defamatory statement.