Having been here I wish that every body just gave you the referral you needed.
We LOVE Dr. Marks at Cook Children's Ft. Worth. LOVE HIM! He has a long waiting list but is absolutely worth it. Don't waste your time with Dr. Mike Rios. He is a developmental pediatrician. I know you were not asking about one of those. Typically at some point in your journey some one will mention looking into a developmental pediatrician and I am just say don't bother with that one.
Here is the web address for your local ECI www.mhmrtc.org. My daughter with hypotonia, did not qualify for services but my daughter with a speech delay does. So it just depends on what other delays you are dealing with and how severe they are. My biggest advice is that if you can afford your private therapy don't trade it for ECI but do both. Once your son gets to school age they don't have the resources that your private therapy has. However if you don't have ECI continuing services once your son gets to school and by services I mean simply having a IEP or a 504 plan in place becomes much more difficult.
At 2 we were concerned with several things we saw with my daughter. Having a family history of Autism that weighed heavily on our minds. We went to ECI and her delays were not "severe" so she did not qualify. So we started OT on our own. It took us a year and 3 doctors aside form our regular pediatrician before we could get 2 to agree on a diagnosis. Now I look back at pictures and wonder how anyone could have missed that my daughter has Cerebral Palsy.
If you have any more questions please don't hesitate to send me a private message. I will be happy to help you in any way I can.