If something hurts like it's been stung by a bee, it hurts stingingly.
Stingingly makes people think of pain, like being stung by a bee.
Examples:
The cold wind blew stingingly in my face.
She felt the rain stingingly on her skin.
The hot soup burned stingingly.
The snow hit my face stingingly!
The spicy food burned my mouth stingingly.
The bee stung me stingingly on my arm.