Medical Center Arlington. Patients now have the option to see an urgent care provider from the comfort of their home. Call 855-694-6682. An Urgent Care Clinic in Arlington, TX and Neighboring Communities. Urgent Care for Kids in Arlington, TX provides after hours walk-in pediatric urgent care in Arlington for patients between the ages of 0 and 21 years … How can I access the expertise of Mayo Clinic? If you are looking for the best family physicians urgent care clinic near your area, the one name that you can completely trust is Arlington va immediate care. Weekends: 9:00 AM - 5:00 PM. /*-->*/.