You do not get the shield's bonus if you are using a two handed weapon.
The first time you equip the complete dragon armour set, that quest is completed, you get some experience points, learn a level of a skill (Elemental Strike or Elemental Hail, IIRC) and Bless is cast on your character (a temporary effect). After that, there is no extra bonus for wearing the complete set.
I do not know if having a 2 handed weapon equipped will prevent the game from counting the shield for the purpose of completing the dragon armour quest (probably not), but if you equip the helm and there is no reaction, you can unequip the weapon or switch to a 1 handed weapon temporarily.