Hi, Welcome to JustAnswer. I am a licensed veterinarian and I'd like to be of assistance. It is very possible that with Kenneth's bleeding from his nose that he does have something up there, and taking him to the vet is very much the thing to do so that this foreign body can be removed and Kenneth will heal up and be much more comfortable.
Unilateral nasal bleeding could also indicate a fungal infection, and, unfortunately, cancer. But if this just suddenly started, then most likely it is a foreign body.
Rhinitis just means inflammation of the nose, but doesn't tell us the cause. Usually, if the rhinitis is infectious (bacterial or viral) both sides of the nose would have drainage and could be bleeding.
"itis" attached to any word means "inflammation of". . .colitis is inflammation of the colon; gastritis - inflammation of the stomach, etc.