You could have a desirable climbing rose or perhaps a wild climbing rose that had started from seed from bird droppings, or the desirable cultivar has died at the ground and you are seeing what kind of rose was used for the rootstock now.. If your rose is growing as fast as you say, fertilizing will only increase the cane growth and create an even bigger plant.
Roses buds form on branches that are horizontal much more readily than those growing straight up. Consider tying or training them in a horizontal direction.
If you feel the plant is really out of control, you could prune it down completely early next spring and start all over. It may take it into the second year to bloom, depending on the kind of rose it is.
Sincerely, Richard Hentschel