I'm glad to read you get happiness from your cats and music, I enjoy escaping with music too.
Diagnosis is something that some people find helpful and some don't (social stigma and 'labelling' as your T described), it seems many T's are cautious about diagnosing too quickly and have to say I agree with caution as misdiagnosis can be something that is harmful, best to be very cautious IMO.
Childhood emotional neglect can happen when parents are caring but wrapped up in their own problems (such as their own MH issues) so not really 'present' for the child. Not to say that definitely did happen to you but it might be something that resonates if you read up on it.
I am so glad to read these posts helped you!