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When you said that the soreness concentrates to the tear ducts, do you mean on the inner corners?
Sorry for the delay. It sounds like you are suffering from allergies/sinus. This would be consistent with the itching, discharge, and discoloration under the eyes. Since the tear ducts drain into the same area in the back of the throat that the sinuses drain into, when this area is swollen, it can stop up the tear ducts and cause them to swell and be sore.
You need to be treated for sinus/allergies with Zyrtec or Allegra or Claritin. If this doesn't work, sometimes we use short doses of steroids.
Hope this helps and thank you.