The drops are ok as well but the problem is that the blood vessels are too close to the skin in the nose. When a child is excited, stressed, playing hard or if the air is dry the blood vessels enlarge and the skin inside the nose cracks. It can cause intense nose bleeds or small ones. With the drops it temporarily moistens the skin in the nose. With Vaseline it provides a constant moisture as well as a thin barrier against dry air.
My nose bleeds were so bad as a child. I had my nose cauterized multiple times and the next stage was surgery if they didn't stop. The specialist suggested Vaseline daily and it worked!! So every night before I went to bed I put Vaseline in both nostrils. I did this for years and never had a nose bleed again.
I had this problem as a child as well, and yes Vaseline works very well. My nosebleeds were always present when I was suffering hay fever, (I had terrible seasonal allergies as a child).