Think of the bottle this way: it was manufactured by a bottle-producing company which sold the bottles in bulk to pharmacies all across the US to hold prescriptions. Today the only difference is that the bottles are plastic. One might be able to figure out the manufacturer of the bottle based on markings on the base. A photo, sketch or rubbing of the base would be necessary..
Pearl Drug is/was undoubtedly a local pharmacy. To research it, most likely you need to go to a local historical society or library. A local library may have old phone books or city directories or newspapers which can help you piece together when it was in business, etc.