Shiny help pokemon Heartgold?

Depends on the moment you've saved the game.

The shininess of a Pokemon is determined along with the rest of the PID when the old man turns to face the road.

If you've saved before that, you can soft reset to go through the procedure of the old man finding the egg, you accepting the egg, and you hatching the egg again, to find a different offspring.

If you've saved after the old man has found the egg, but before you accept the egg, you'll get the same PID (shininess, nature, ability, and gender), but with different IVs.

If you've saved after accepting the egg, but before hatching it, you get the exact same Pokemon.

I think you can but there is no need! If you reset it's basically just like hatching a new egg! The shiny rate will be the same. I recommend my way though. Hope I helped! :)