No. Never. Taking on the role of "internet doctor" is not only unsafe but can become distressing if you make yourself believe you have a diagnosis that, in reality, is inaccurate. There are many illnesses, disorders, and mental health issues that have overlapping symptoms. As others have said, it is never a bad idea to question the diagnosis you have been given and share the information of another diagnosis you feel is more accurate. They will ask you why you believe it to be accurate and will either agree with you or explain why it does not fit your case.
It is absolutely possible for T's to give a wrong diagnosis and I am going through the hell of that right now! So I encourage everyone to ask questions and challenge the answers. It's the same thing with doctors...one may diagnose you with food poisoning while the "second opinion" may not agree and sees it best to do further testing.