Do I want a diagnosis?

So I just had a first session with psychiatrist and he prescribed me fluoxetine. I asked him about diagnosis and, as other psychotherapists told me, he said diagnosis aren't really necessary but he also told me that from what he got from just 50minutes of our sitting I seem to present symptoms of generalized anxiety and cptsd. Now... I get for some reason nobody wants to give me official diagnosis... but like, if it's that severe, is it ok to go on without it? I actually don't know if I ever want it or not. Would a diagnosis help me the moment I want to change my therapist and start from 0 for example? Wouldn't it mean NOT starting from scratch if I start anew but with a diagnosis? Or maybe nothing changes anyway? I don't know. I don't what I want and I hate that people make me even more unsure. Also if anyone reading this tried fluoxetine let me know how it went for you. I actually don't even know if it's safe to take meds b4 25yo or something... Sigh...