I too have seen this second sun... Last summer I was floating in our pool with sun glasses on, and noticed something just off from the sun. I know this is bad for my eyes but I grabbed 3 more pairs of sunglasses so I can get a better look at the object. Sure enough it was something totally separate from the sun.

I am still unsure whether or not it was the moon, but it was just off to the side of the sun.

So kudos to you on this man