Is it permissible to consult a psychiatrist for the treatment of Obsessive-Compulsive Disorder, given the concern that this might contradict the belief that healing comes through religion and not medicine, and would seeking medical help in this case be considered an act of disbelief or a sin?

Mental illness or obsessive thoughts are treated with Ruqya (Islamic exorcism), while consistently observing adhkar (remembrances) and supplicating sincerely and devotedly. Also, by consulting a psychiatrist and taking the appropriate medication. Both approaches are permissible. The Prophet, peace and blessings be upon him, encouraged seeking medical treatment, and there is no contradiction between Ruqya and consulting a doctor. As for recommending a trustworthy psychiatrist, you can ask people of knowledge and experience in your country.