Are Catholic priests allowed by church law to provide professional counseling and referrals to penitents who come to them to confess?

Let us say we have a priest, who is a licensed psychiatrist as well. A devout Catholic confesses their sins to said priest. The Catholic person chats with the priest, and priest asks follow-up questions like a doctor would. Priest then determines that the person is suffering from a psychological disorder, in this example, depression. From a professional/moral standpoint the penitent/"patient" should not be obligated to pay the priest for his profession, since they came to confess, not to seek medical help. But as the priest orders penance, is the priest allowed by Church law to disclose to the penitent his diagnosis, offer counseling, and/or suggest to the latter to at least seek another psychiatrist for a second opinion?