Step 1: Understanding the concept of antacids.
Antacids are substances that neutralize stomach acid (HCl) and provide relief from acid indigestion. Common antacids include hydroxides, carbonates, and bicarbonates of certain metals.
Step 2: Analyzing the options.
(A) Al(OH)$_3$: Aluminum hydroxide is a commonly used antacid that neutralizes stomach acid.
(B) Mg(OH)$_2$: Magnesium hydroxide is also a common antacid that is used to relieve acid indigestion.
(C) Na$_2$CO$_3$: Sodium carbonate (soda ash) is not an antacid and is not used to neutralize stomach acid. It is alkaline, but it is not commonly used in medical treatments as an antacid.
(D) NaHCO$_3$: Sodium bicarbonate (baking soda) is another commonly used antacid.
Step 3: Conclusion.
The correct answer is (C) Na$_2$CO$_3$, as it is not an antacid used for neutralizing stomach acid.