In other words, is there any objective test to find out the problem or differencce of a patient from blood test, CT scan etc rather than assessment by a list of questions or symptoms that we cannot objectively measure or see e.g. feel nervous, feel sad, feel bad

You can find your answer to your question at this site right below the heading "Getting A Diagnosis":

https://www.nami.org/Your-Journey/Individuals-with-Mental-Illness/Understanding-Your-Diagnosis