Yes, I would go to a specialist, also, like the other poster suggested, put some cream on the inside, you could have some dry skin inside your nose. Also, take bio-flavonoids, these, along with Vitamin C, will help to strengthen the capillaries in your nose and other parts of your body, sounds like they are also thin and need some help to be more elastic, etc.
I get the same thing, on one side only. i cant blow my nose too hard it will trigger it. An ENT said to put a small dab of polysporin in my nose, and if it continued it would have to have it corterized. i have not had that done since it is manageable.