My two month old had her shots today and is now running fever. What causes this to happen? At what point should I be concerned?

Mild reaction. The immune system is working, that's why she got a fever. Be concerned if the fever is over 105, if she cries continuously for more than 3 hours, or convulsions without fever within 3 days of the vaccine. A low grade fever should be treated with tylenol (acetaminophen). Soreness of the injection site should be treated with tylenol (acetaminophen) too.
See Dr Levey's. And remember that a mild fever does not suggest that the next immunization should be withheld !