There are different reasons that may make you get a constant ring in your ears, like tinnitus. It can be caused by too much wax, an infection or a hole in the eardrum. It would be advisable to get a check up to get rid of the ringing sound.
I dont know your age, but they are right, it is called tinitis, but such ringing can also be caused by high blood pressure, or certain inner ear infections, or even damaged bones which make up the ear. In any event see a physician to rule out the more serious causes, it just may save your hearing. Good luck.