"My pigs are killing me!"

Actually, I believe it refers to the person's toes, rather than the feet themselves.

It is a reference to the old nursery rhyme This Little Piggy, which is typically done while playing with each of the child's toes in turn.

I've seen a Looney Tune cartoon or two where it is used in this sense, and the given Wikipedia link mentions several. Most often a cartoon character almost falls off something, is hanging on by his toes, and the protagonist evilly plays "this little piggy" while pulling up the toes one-by-one.

I think it has to do with the use of trotters as slang for feet, as can bee seen in this entry at Dictionary.com

trotters noun - 3. the foot of an animal, especially of a sheep or pig, used as food.

And further down the page in the slang section

noun the feet. : Sit down and give your trotters a rest.

So it seems likely that usage has gone backwards from trotters to pigs feet to pigs