Nope, this is non-pollination (established papayas are very hard to stress).
Can you describe or post a photo of what the flowers looked like? Were they on long stems, on short ones? How many stamens were there? What colour were they (cream, yellow, white)? This will help us determine the gender of your plant. It sounds like you've got a female, which means you'll either need a male or a hermaphrodite to make it set fruit.