Can I Get an Autism Assessment Without a Formal Diagnosis?

You can try to speak with a therapist? I been told you can do evaluations with them.

If you do not use insurance for the evaluation, then it won't be on a public record or shared health care record. If you need the results to obtain benefits or adjustments, though, you will likely need an official diagnosis.

It varies it is best to talk to a professional about it

I live in the USA (state laws may vary) but as far as I know my diagnosis is not shared with anyone unless I choose to do so.

I can definitely understand worrying about the stigma with medical doctors. Especially if you're afab or female presenting. Where I live medical doctors weren't able to see what a therapist or psychiatrist diagnosed you with until a new law passed. You'd have to look into the laws where you live, but you might be able to get a diagnosis without worrying about how it would effect doctor appointments for your physical health if that's what you're worried about.