If you are not 100% satisfied with your doctor's explanation, then YES, you should consult another doctor.
However, I also know of several other people that have experienced profuse nosebleeds at some point in their lives. This is what they figured out:
This condition could be due to "thin" blood vessels / membranes in your nostril. You get a nosebleed because there's a cut in your nostril's membrane. Once there's a cut, it's quite difficult to heal. You're inhaling and exhaling air and that tends to dry out the membrane. A dry membrane will easily crack again and cause further bleeding.
So: get some vaseline or Vicks Vapor Rub. Put some on your finger and coat the insides of your nostrils with the ointment. This should be repeated whenever you feel your nostrils drying out. If you do this over a sufficiently long period of time, your nostrils won't dry out and will have a chance to heal.
Other than that, stay away from blood thinners.
Hope that helps,