What you describe appears to be allergic conjunctivitis, although one cannot discount the possibility of a condition called blepharoconjunctivitis.
In allergic conjunctivitis, the eyes and eyelids become swollen, the eyes become teary and there is significant itching and sometimes pain. It is usually triggered by environmental factors such as dust or pollen. The treatment includes anti-allergy medications such as Pataday, Alrex or Optivar and cool compresses. Avoid rubbing the eyes as this will only worsen the symptoms.
In blepharoconjunctivitis, many of the above symptoms are experienced, but, in addition there will be a crustiness of the lid margins along the base of the eyelashes and you may wake up with the eyelashes stuck together, as you described. The treatment includes, washing the eyelid margins with baby shampoo to remove the crustiness and antibiotic ointment for nighttime use.
I believe the most likely diagnosis is allergic conjunctivitis. Of course, there is no substitute for a complete eye exam to confirm this. The condition is usually seasonal, but in some patients it can be present year-round if no treatment is sought.
I hope this is helpful....