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Same with our four year old son at the time. All the general practitioners, pediatricians and service providers (10-12) had no clue what Autism entailed, as all the core symptoms were there if they wanted to look for it, and after we told them about it. Even after we told them our older son had Autism, and to please screen for Autism in Dylan, as he still was nonverbal, had severe eating and other sensory issues, and some routines and atypical fascinations, they still all basically had the attitude, "We cannot evaluate him for Autism. We do not know how too" or "Let's wait until later" attitude.
All they would ever do is look in his ears, up his nose, in his mouth, and check his height and weight, and disrespect us there. He was always between the 1 and 5 percentile! And delayed in all areas. They could not put the pieces together, or want to, as they are not trained to evaluate Autism, or as they are too superficial as Dylan had eye contact, a smile, and had no atypical physical features. He did though do hand flapping in their presence. So, after we self-diagnosed him ourselves, using common sense and after additional research, we took him to an Autism specialist 4 hours away.
We brought video of his behaviors in all environments, and one hundred pages of additional evidence that that specialist looked at in advance of the appointment. This was needed as at the appointment Dylan refused to be examined and get out of his stroller. He sat with his IPad with minimal eye contact and randomly played with his IPad app programs, some repetitively. He would scream at any attempt to get him out of the stroller. That was because this was a new place for him, and a new doctor. It was not his routine to get out and play there, so why would he tolerate or want that? That doctor within 45 minutes of seeing him told us "Your son definitely has Autism."
Our vast family experiences show most non-specialist doctors and service providers to be not at all capable of evaluating for Autism, as seen by their own words and practices, so for those who want formal diagnostics, to rule in or out Autism, go to a specialist with much training in Autism. They are trained to see the fine and even subtle nuances of that condition.