Dry cough, and the back of my eyes hurt. Anybody have any ideas for relief?

Cough with eye pain. Many possibilities. Sinus problems cause back of eyes pain and post nasal drip with a cough. Can be several other things. You need to call your doctor for a check up.
Likely sinus. If you have a cough and pressure/pain behind your eyes it is likely secondary to sinus congestion. If this continues for more than a few days see your pcp for further evaluation.
Etiology... In order to effectively treat your cough, the etiology must first be determined. Possibilities include bronchospasm from any etiology, gerd, sinus disease or a combination of factors. See your doctor for evaluation and treatment.