hi Sean ben Noach.
My daughter has similar challenges but they are improving with age. It would be a good idea to go ahead and have the testing. In various states and cities programs and services are available but require an “official” diagnosis. The sensory issues, in our case are related to receptive issues. that is the ability to understand, process and prioritize information. A different version of this manifests itself in expressive delays. That relates to the ability to communicate. both of these are within the spectrum and can co-exist with other common symptoms. some of these symptoms or issues are more than visible at home and can be concealed in public. be patient with people who do not believe you when you tell them your experiences at home with your daughter.