If it is pinky eye (conjunctivitis) it is either viral and just has to run its course or bacterial and can be treated. Sulfa meds, like Albon can be somewhat effective against the bacterial strain, and sulfas are synergistic with tetracycline (LA 200 or Tetradure), they help each other work better/faster.
If you are having any "cold" symptoms in your herd, that can cause the redness and discharge, too. Also, the deer may have gotten dirt or other matter in it's eye and be irritated from it.
If you decide to use any type of eye ointment - DO NOT use one with a steroid in it. If there is any scratch or abrasion on the eye, the steriod can cause damage to it. Make sure it is an ophthalmic antibiotic/antibacterial ointment only.