Hilar Prominence on my Right side.

Typically nothing good, sorry to say unless nothing comes out of investigations. Many things can present this type of reading on a Chest x-ray, since the hila contains blood vessels, the bronchial tree, lymph nodes, and other structures. Possibilities include an acute vascular process like an aneurysm, a malignancy (lung or lymphoma), pulmonary hypertension, infection, sarcoidosis and the list goes on. It really depends on the clinical situation, patient age, and other diseases present. It is not to be ignored, and while it may turn out to be nothing significant, it really must be worked up with further testing, the next step being a CT-scan or more specific and sensitive diagnostic study depending upon the clinical symptoms if any.