Swine flu and mad cow disease both take their common names from animals. The swine flu is a strain of the influenza virus that was first identified in pigs, while mad cow disease is otherwise known as prion disease, a condition that can be spread by exposure to protein particles from infected cows. These two diseases are not related in any way--the swine flu is a virus while mad cow disease is a very rare condition because it is spread by a protein particle, not by a bacteria or virus like most diseases.
As you point out, there is a connection between both conditions in that they can be spread by animals or exposure to them. However, this does not mean that every pig or every cow is a potential carrier. The swine flu influenza strain was first identified in pigs, but it became a human health concern once the virus started infecting people. The vast majority of people who became sick with the so-called 'swine flu' caught the virus from another person. The best way to protect yourself from getting swine flu is to make sure you receive your flu vaccination every year.
Mad cow disease is also very rare. It is thought that cows initially linked to spreading the disease in people (mostly in the UK and Europe) did so because the cows were fed animal feed containing tissue from other cows that had died of the disease. This caused significant changes in animal husbandry practices.
You should discuss this and other general health questions with your physician. He or she can provide more information and direct you to further helpful resources.