Are there effective over-the-counter medication to reduce hemorrhoid pain?

Yes: Over the counter steroid creams and preparations of Benzocaine (especially mixed together) when applied on, around, and up the rectum can significantly help hemorrhoid pain (usually).

Not really: Most over the counter medications only temporarily improve hemorrhoids. Ice and sitz baths (soaking in warm water), as well as avoiding constipation by increasing fiber and fluid intake, work just as well for less money. Also try a moisturizing cleanser like balneol to decrease your irritation when wiping. Wipes and plain toilet paper can be really irritating.