Itching with elevated bilirubin may suggest that there is an obstruction in bile flow that most commonly occurs with gall bladder
pathologies, and is usually gall stones
A detailed liver function test (LFT) would have helped to secure this diagnosis if the alkaline phosphatase
was also raised.
But as you mentioned no obvious jaundice, it is important to know that the other LFT parameters such as the enzymes are normal.
liver/GB is important at this stage.
Antihistamine will lower the itch but if this liver/GB related itch you will need medications like cholestyramine
that should be prescribed after a visit/consultation with a gastroenterologist.