I've had the exact thing going on with me...
I`ve been at alot of eye doctors which couldn't why my right eye tends to get more allergies then my left( i thought it couldn't be as a result from allergies).
but after doing a ct( to check if i got something wrong with me, i also have pressure in forehead and around eyes) the ent said the ct was fine.
The allergiest said it's logical to have more severe reaction in the right eye.. but did not tell why.
so I don`t wanna bummer you but I think they won't find anything in particular and you can save yourself the carcinomatous radiation.
Btw: I was suffering from this problem like all my life, but did not do anything to take care of it cause i thought it's normal to suffer from such eye pain itchiness and burning, and now I just can't live without trying fixing my health to live as a normal painless person