Once the psychiatric services have formed an opinion of me, is it possible to change their mind?

Sure: "psychiatric services" are composed of individuals who tend to have varying views about problems and people. It sounds as though you may have found yourself in a situation where for one reason or another you find yourself in a struggle to make some point... That struggle might be part of the problem. Mental health professionals tend to be resistant to pressure to agree with a conclusion.

Psychiatry: Once a clinical opinion is formed its for that day usually in civil settings not forensic, there is ur and insurance monitoring the necessity of a patient to stay in a psych hospital clinical opinions are dynamic and based on your treatment response.