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What test could be performed to ensure she is prescribed a pair of glasses that would relieve her symptoms?  And how does this test work?

The clinical vignette implies that this young patient may be overminused and thus may be experiencing asthenopia from ciliary spasm.  Since the patient is refusing eyedrops including cycloplegic eyedrops, we cannot inhibit her accommodation pharmacologically.  One method that can be used during the manifest refraction to prevent overminusing the patient is the duochrome test.  This test makes use of the existence of chromatic aberration of the eye, whereby shorter wavelengths of light (e.g. green) are focused in front of longer wavelengths of light (e.g. red). 

The duochrome test consists of a split red-green filter that makes the background of the acuity chart appear vertically divided into a red half and a green half.  With optimal spherical correction, the letters on the red and green halves of the chart appear equally clear.  The commercial filters used in the duochrome test produce a chromatic interval of about 0.50 diopters between the red and the green.  When the image is clearly focused in white light, the eye is 0.25 diopter myopic for the green symbols and 0.25 diopter hyperopic for the red symbols.  When performing the manifest refraction for the patient, if the patient states that the letters on the green side are sharper, then she is overminused and thus more plus power should be added.  Conversely, if the patient states that the letters on the red side are sharper, then she is overplused and thus more minus power should be added.