Why is One Eye Bigger and 'Higher' Than the Other? (photo)

From your photograph and physical symptoms it looks and sounds like Graves Disease. It is common in this condition for an eyelid to retract upwards giving the startled appearance. After 1 year of stable appearance, the eyelid can be repaired by an oculoplastic surgeon. Artificial tears may be needed to prevent dryness. See your internist for some blood tests including thyroid function.  

You have a very minor degree of asymmetry if your eyes, which is not uncommon at all. I would consider the degree of asymmetry to be within the normal range.  However, it sounds like you have some other issuers which should be looked into further by your primary care physician.