Shield has a somatic component and you only have one reaction per round
Everything else works though. Just to run though the list; wearing studded armour sets your AC to 12 + your Dexterity modifier of 3. In one hand you hold a shield which adds +2 and in the other you hold a finesse weapon with which Defensive duelist can add a bonus equal to your proficiency (ie. +2) as a reaction for a given attack. However, both your hands are occupied meaning you have none left to provide the somatic component (S) of shield. Also, you have used your reaction with Defensive duelist, which means you haven't got it available to also cast shield.
You can of course solve the first issue by picking up the Warcaster feat using its second benefit:
- You can perform the somatic components of spells even when you have weapons or a shield in one or both hands.
At which point you will have to choose between using shield and Defensive duelist. Note that the bonus to AC from shield will be higher until you reach 13th level, but does cost one of your precious spell slots. Shield does however work until the start of your next turn, and not just on the singular attack.