Is it possible to have itching by internal hemorrhoids but no bleeding?

Just hemorrhoids ?: Are you sure you have just hemorrhoids? Pain +/- pruritis (itching) from the rectum that recurs may also indicate anal fissures, proctitis (due to infection, inflammatory bowel disease, radiation therapy, stercoral ulcers, rectal prolapse, trauma, etc.), prctalgia fugax. Depending on your age, risk factors, current medication (aspirin, nsaid's), circumstances, you will want to get evaluated.

Yes: Internal hemorrhoid without significant thrombosis may causing chief months painless or painful bleeding, discomfort, tenesmus, with leakage of fecal material. Bleeding occur from the internal hemorrhoid when there is significant dilatation of the internal hemorrhoidal veins which may accompany with thrombosis of the hemorrhoidal veins, leading to rectal bleeding and pain.