Sounds like it could be Laminitis but I thought it usually affected the front feet first. Its basically Founder like what is commonly seen in horses. Things that can cause Laminitis are overeating or sudden access to concentrates. Basically too much protein at once. It can also develop after an infection but I think thats pretty rare. Most of the time it is caused by too much concentrated feed. It is not curable but can be managed with proper diet. Reportedly, soaking the foot in ice water as soon as you notice it is hot and swollen can help to reduce any permanent damage done to the foot.
Here's some treatment info I found on the web.
Here's some treatment info I found on the web.
A good link with in-depth information. http://www.tennesseemeatgoats.com/artic ... goats.html