How is your vision? Is there mattering and/or crusting in the morning?
It does sound like allergy. However, what the allergy can do is to loosen the white part of the eye so that it swells up and sometimes hangs over the lower lid. This causes redness and swelling. I think what you need is some ointment to put in at night right before bedtime. This will help to protect the eye while you are sleeping. If you can, turn off and ceiling fans at night and humidify the air in the bedroom. Sometimes, while asleep, the eyelid do not shut tight and this leaves the eye exposed to air and dries out as well.
What made him think that there is a tumor? Is the swelling hard and firm like a nodule? Or is it soft?
Artificial tears come in ointment form (like Genteal gel or Lacrilube). These are OTC. I can't really comment on the CT since I can't see or feel the lids.