It will vary from state to state, but in New York I had no out of pocket expenses thanks to Medicaid (Fidelis). However, I was also able to verify at least one instance of childhood injury likely resulting from poor motor skills, and that seemed to help move the initial process along before testing began.
A good starting point is to find services in your area and contact them, by email if necessary, to begin the process. For example, I used https://aapsa.net/
As to whether or not it is worth the effort to get a diagnosis, that depends on a number of factors. In general though, I would say that it's worth making the attempt, if for no other reason than to have that opportunity of being assessed professionally, so the nagging suspicion can be confirmed or allayed. It may be that you are autistic, but that you have comorbidities as well, which of course would be important to know about.
The bulk of funded programs are reserved for those who are under the age of 18 and in need of assistance at school, or considerably low on the spectrum, at least that was the case in New York state. But in my case Medicaid would have even covered the transportation needed in getting to and from appointments. That said, I received my diagnosis in 2015; things may have changed significantly in the years since.