contango 

Check the position of your saddle. If it's too far back you may be leaning forward too far and putting pressure on your testicles. If the problem is more the perineum area that sounds like you're sitting on the narrow part of the saddle rather than the wider part, which also suggests the saddle might be too far back.

It's also important to get the angle of the saddle right - if the nose is too high it will tend to cause you to crush your testicles into it as you lean forward for the bars; if the nose is too low you'll tend to slide forward on the saddle, putting your weight on the narrow section. A tiny change can make a huge difference - a while back I was aware I had to keep sliding myself back on the saddle so I raised the nose by a little over 1/4" and found it was too much, I had to take it down a little.

Also consider what clothing you're wearing. I only started wearing cycling shorts fairly recently - my first ever century was on a mountain bike with regular clothing, platform pedals and regular training shoes. But I had worked out that some of my underwear was tight in ways that really didn't work on a bike, and some was loose in ways that caused it to soak with sweat and bunch up underneath me (which was as unpleasant for me to ride on as it probably was for you to read about). Padded cycling shorts aren't essential by any means but do make riding so much more comfortable you won't want to go back.