I found this little bit of information.
Swollen testicles may occur as the result of bruises, kicks or stings, and the trouble frequently happens to stallions during breeding season.
Bathe parts with warm water, then apply Badger Balm, thoroughly rubbed in, and follow by the use of the Antiseptic Poultice. This is done by placing a wide bandage around the belly, just in front of the hips, then attaching another strip to it just at the point of the sheath; bring up between the thighs and along the side of the tail and fasten to the other strip just over the loins or kidneys. In this manner a poultice may be applied easily, and its use is very important in such cases.
Is anything swollen on the mare? Is your stallion I pain, or is he just swollen?