My grandson has similar issues to your son. His behavior is related to a sensory processing disorder. The school district is required by Federal Law to provide evaluation and treatment for any child who is having difficulty in school. My granddaughter's teacher and pediatrician suspected that she was ADHD and the school district evaluated her for that and the school provided a tutor for writing. She's now on target, is no longer is taking medication and is having success in school.
The office that does the evaluating is a county entity. You can find them in the phone book under co. name Education School District Office or ask about them at the school. Their services are free. They involve the parents at every step. The parent has the right to accept or reject their recommendations.
My daughter has been pleased with the service they have provided for her and both of her children. My grandson was unable to be in a group when he was 4. The school district put him in a therapeutic preschool and he's now in a special education class. He has more serious issues than those described for your son. He wouldn't have lasted in a regular kindergarten or been passed to first grade. My granddaughter was doing OK in school but obviously having difficulty. Both have an IEP (Individual Education Plan) which has made a great difference in their levels of success. My daughter will most likely not need a special plan in this upcoming year.
So.....I highly recommend that you make an appointment for an evaluation. Then you can go from there in deciding what to do. You can take him to a private person for evaluation. However, he will probably need to be seen by more than one professional person which takes time. The school district has all of these people in one place. The evaluation is completed in a couple of weeks.