My 7 year old has had a cough now for a little over a month. I have tried OTC cough medicine but they do not work. Should I call her pediatrician?

Yes. List of causes for the prolonged coughing is lengthy. Detail history and thorough physical exam are essential to sort these out.
Absolutely! If the cough has been there nonstop for that long, it's time for her to see her doctor. There are a variety of causes of persistent cough, and each is treated differently from the others; the only way to know which it is would be to have her examined. I hope you find the cause easily and that she feels better soon !
Yes. Has she had an chest xray? Some times children are prone to swallowing or aspirating objects. They might not even recall the incident.