A quick response for now. You can have him evaluated thru the Intermediate Education Service District in connection with the school district. Evaluation is free and mandated by law. They will look at him as a whole child and be seen by more than one specialist.
The school district is then mandated by law to provide any assistance that he may need in order to be successful in school.
You can still have an evaluation with a private specialist at a later date. But by connecting with the school district he will be seen within a week or two and you'll have an idea of what is going on. And the office and you will formulate and IEP (Individual Education Plan) which will help his needs to be addressed sooner rather than later.
My daughter, who has ADHD, has an IEP which provides for a writing coach during school hours. Otherwise she's in a regular classroom. There is no stigma involved as there was whenever a child was different when I was young, 40 some years ago.
My daughter has been working with the Intermediate Education Service District with her son since he was 2 1/2 and has been happy with the evaluation and services provided. I think that using private services may provide a more intense evaluation and treatment but as you said it's expensive.
My grandson has received some services thru his insurance, Kaiser Permanente, and was seen immediately once the school district finished their evaluation.
You can find the phone number for your county's Intermediate Education Service District under your county's phone listings at the front of the phone book. Or you can get the number from your school district office. Your son's school may also have the number and be able to discuss it's services with you. Or his pediatrician can give you the number. My grandson got started when his pediatrician gave his mother their phone number.
I highly recommend that you get started as soon as possible. Start with The County Education Service District. They will consider all of your concerns. It's quite possible that the all 3 are related. If there is any concern that they cannot address they will tell you and recommend a place for you to go to get help. You can also get involved privately once your son gets an appointment off the waiting list.