If your pig turns into a Flu Pig, there's no way to turn it back to its original breed. It's best to ship it right away.
Check the status of your pig if you can; "Your pig doesn't look well" means the pig is about to become a Flu Pig. See below for what you can do to prevent your pig from becoming sick*:
1. Always remove poop (reduces chances of pigs becoming sick)
2. Sell Flu Pigs right away (otherwise it will spread to the other pigs)
3. Vaccinate your pigs (100% effective)
Cleaning poop is vital in preventing your pigs from becoming sick. Note that your pigs may still become sick even if you install a Poomba, Cleaning Pig, and Air Conditioning. While these reduce the chances of your pigs getting sick, they are not 100% effective. If there's a pig that you definitely don't want getting sick, it's best to vaccinate it.
*Your pig will not get sick if it's vaccinated, but there may be poop left in the pen.