Carousel Pediatrics Austin and Round Rock, TX. Call Carousel Pediatrics TODAY at 512-744-6000 to get an appointment before the BACK-TO-SCHOOL RUSH in AUGUST! Our appointment slots will fill quickly. Our Medical Director, Dr. Azadi recommends that families bring their children in to getcaught up on any vaccines that were missed in the last year.Locations‧Contact Us‧Services‧Southbrook‧Springdale‧Careers.