If we consider for a moment the reaction of lithium aluminium hydride with the carboxylic acid then the first step will be the reaction of the carboxylic acid with the LiAlH4 to form a carboxylate anion.
Now due to the resonance effect both of the oxygens are the same, thus there will be no difference in reactivity between the carbonyl oxygen and the hydroxyl oxygen in the carboxylic acid.
There is another problem, consider for a moment if you were to make an isotope labelled carboxylic acid where the C=O oxygen is O-18. The other oxygen is O-16.
The problem is that due to the autoioniziation of the carboxylic acid that the carboxylic acid hydrogen will be able to move between the two oxygens.