Thanks for the query to H.C.M. Forum.
Fatty infiltration usually if non alcoholic don't produces pain.
As you mentioned pain on the right side of abdomen ( might be just below the rig cage).
Sometimes I have seen that this type of pain usually associated with lung 's lower lobe ( may be thickened pleura or friction of pleura or pleural effusion
In your query emphasis is over only LIVER
, so think about other disease also.
Physical examination is very important so consult one more physician and get his opinion ( 2nd).