Step 1: Check each statement.
Analgesics are classified according to their
\[
\boxed{\text{pharmacological effect}.}
\]
Hence, Statement I is correct.
Sulphonamides are classified according to their
\[
\boxed{\text{chemical structure}},
\]
not on the basis of target molecules.
Hence, Statement II is incorrect.
Antihistamines are classified according to their
\[
\boxed{\text{drug action}.}
\]
Hence, Statement III is correct.
Step 2: Choose the correct statements.
Therefore,
\[
\boxed{\text{Statements I and III only are correct}.}
\]
Hence, the correct option is
\[
\boxed{(B).}
\]