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Unfortunately, many people who have an allergic phenotype, or predisposition (meaning they have had and do have significant systemic allergies for years) get what we call "allergic shiners" which are these dark circles under the eyes, that give the appearance of tired eyes and appearance. Unfortunately, even in most patients who are on every kind of allergy treatment known to man, these dark circles will still persist and there isn't really any treatment for them that's been known to make them go away.
About the best advice I can give you is to be on every kind of local and systemic allergy treatment that you can be on to help control your body's response to allergies. This would include an oral antihistamine every day (such as Claritin, Zyrtec, or Allegra), a leukotriene inhibitor like Singulair every day, a nasal steroid such as Flonase or Rhinocort daily, and if you have asthma, to use an inhaled steroid.
You're correct the allergy drops are useful in allergic conjunctivitis, so if you do get this, then it would be helpful to use those as well to help control this process on a local level.
Does that make sense?