Can you use spells or abilities on your own shroud creatures?

Not if the spell or ability calls for you to target that permanent, shroud will prevent you targeting it, even if it's you own creature.

However, effects that don't call for a target can get around this such as 'Choose a creature', 'Whenever a creature', 'Target player sacrifices a creature' or any effect which works én massé with the Word 'all' such as Wrath of God.

Examples: Graft, Wrath of God, Conspiracy, Overrun, Diabolic Edict

These examples would all still affect a creature with shroud.