Step 1: Know what histamine does.
Histamine is released in the body during allergies and inflammation. It affects blood vessels, the nose and the stomach.
Step 2: Check Statement (I).
Histamine widens blood vessels, so it is a strong vasodilator. Statement (I) is correct.
Step 3: Check Statement (II).
Statement (II) says histamine lowers blood pressure by narrowing vessels. This is wrong, because histamine widens vessels, it does not narrow them. So Statement (II) is incorrect.
Step 4: Check Statement (III).
Histamine causes swelling and a blocked nose during colds and allergies. So Statement (III) is correct.
Step 5: Collect the correct ones.
Correct statements are (I) and (III). Statement (II) is the only wrong one.
Step 6: Match with the options.
The set that holds (I) and (III) only is the right choice.
Step 7: State the final answer.
The correct combination is:
\[ \boxed{\text{I and III only}} \]