I've had good experiences with the ARC dr.'s in Round Rock, I haven't noticed if they take medicaid. Dr. White is nice though a bit quiet, and doesn't look down on us for asking questions.
I feel like I can go to the dr, tell him what I've done so far about each concern, and he will give me advice on what to do next.
In the past, when I've had a dr. I didn't trust, my strategy was to bring someone else with me. They might run over me- but not my husband or mother.
For the speech issue, have you had your daughter tested by the schools? They will do this starting at age 3 and provide free therapy to help kids prepare for kindergarten and be able to communicate with the teachers.
My advice is which ever dr. you choose, let them know when you schedule that you have several concerns, take a written list of questions, have in mind what you want(like a referral to an ear/nose/throat or eye specialist), take a friend with you, and take notes. You know your child the best and would do anything to keep her safe, and they should not just dismiss your concerns.