Enhanced defense requires: A suit of armor or a shield, and says
A creature gains a +1 bonus to Armor Class while wearing (armor) or wielding (shield) the infused item. The bonus increases to +2 when you reach 10th level in this class.
Repulsion Shield requires: A shield and an attunement slot, and says:
A creature gains a +1 bonus to Armor Class while wielding this shield.
As you say, only one infusion may be cast on an item at a time, but if the Artificer has infused their armor with enhanced defense and their shield with repulsion shield, there is nothing to prevent both of these bonuses being applied to the Artificer's AC. These 'stack' in the same way a PC might have Plate Mail +2 and a Shield +1 and receive the magic bonuses for both. Your calculation of AC23 at 10th level is correct.
In the party I run, the Artificer is the tank, uses specifically this combination to achieve an AC23, and then further casts Blur to have attacks on him made at disadvantage and uses Thunder Gauntlets to have attacks on others made at disadvantage. It is a powerful combination but legal. Fortunately they are currently in Rise of Tiamat so I have lots of Saving Throw based attacks (rather than attack roll based attacks) to target him with.