The diagnostic processes and who is involved in them are things that seem to differ between countries. My evaluation involved psychiatrists and psychologists, with the psychiatrists having the final say, since ASD diagnoses here are only of official value - if you want to file for benefits or services funded through taxes - if they come from a psychiatrist. Thus, psychiatrists who specialise in the autism spectrum are also, on average, the most reliable group of medical/psychological professionals to consult if you do want a diagnosis, where I live.
Even so, all professionals are not equal. People, on a more local discussion board than this one, have reported flying under the radar even for so-called experts, only to get their ASD diagnosis years later and/or from someone else. Some who were diagnosed and confident about their diagnosis being correct were later in therapy for random or related issues (e.g. depression), only to have their therapist disbelieve their ASD diagnosis. It is worth noting, though, that these people pointed out that the therapists who didn't believe they (the patients) were on the spectrum did not themselves specialise in ASD and treated persons - not specifically autistics - for depression, anxiety or something else, without any involvement in diagnostic processes around ASD.
Ignorance is still rampant, sometimes even in places where you would expect some basic knowledge as a matter of course. So my advice is to always, always, always look for someone to diagnose you who specialises in ASD. Personally, I would rather recommend waiting for as long as it takes to get diagnostic appointments with sought-after and hard-to-get specialists than with any random mental health or medical professional who may or may not know even the basics and may, in some cases, be operating on little more specialised knowledge than the general public, as far as ASD is concerned. Although there certainly isn't any shame in not knowing everything - mental health, psychology and medicine are vast fields! - many professionals are, both in my personal experience and from what I've heard from others, unwilling to own up to not knowing enough in certain areas to diagnose and treat you themselves, and those may well misdiagnose you and offer wrong (and sometimes detrimental) treatments. (And that doesn't just go for ASD, but for pretty much any medical and mental health issue.)
Sorry for the novel, but these issues are something I could write a book about.
Now, for 'flying under the radar' - that appears to happen mostly when diagnostic processes are too short, especially when someone tries to diagnose you in a single session, and if you have something that, on the outside, resembles a 'normal' life: a job, a partner, perhaps hobbies that take you out of the house, and if those things work, as in: your world isn't crumbling before your eyes. I've heard of it happening that even specialised professionals can then sometimes mistake highly developed coping mechanisms for normalcy, and the constant stress from having to cope (rather than just function as an NT would) for social anxiety or the like.
I can tell you from the local message board, though, that many, many people share your worry about diagnosis and think that they'll embarrass themselves by asking to be evaluated for ASD, that they'll be considered impostors, someone who doesn't know what real problems are... the list goes on. It's a common worry among some who are self-diagnosed, but, for one thing, very many people who got diagnosed as adults were self-diagnosed first, since ASD isn't often caught in adults who (can or are pressured to) keep their act together unless they outright ask for a diagnosis. And furthermore, if you didn't get a diagnosis of ASD, you might well get another one that you could then accept or reject, and that might help you find what it is that's going on with you.