I've always battled anxiety. As a child I can remember being anxious, nervous, throwing up from anxiety and nervousness over the smallest things, like getting ready for school or being afraid that I was going to forget my lunch in high school (because it happened once- in first grade!!). This was in the '80's, and there wasn't knowledge of childhood anxiety and depression as there is today. I didn't have the option of taking medication.
Looking at it as an adult and parent now, I would have definately taken meds. If my daughters have the kind of anxiety that I did I will do anything in my power to make them feel better, including medication if that's the path that we need to take.
You've done counseling, and if it isn't working you need to try things that will work. Don't worry about what others will think/say. This is about what's best for your daughter and allowing her to have the most normal life (and childhood) that she can. As an adult that has had the experiences that your daughter is having, I would try the medication. 100%.