моля, не сте задали стойностите за последните два параметъра, затова проверете по-долу
try{
Connection conn = DriverManager.getConnection("dbinfo");
String query = "UPDATE Patient SET
PatID=?,FirstName=?,LastName=?,Address=?,City=?,Phone=?,MedID=? ` `WHERE PatID=? AND MedID=?";
PreparedStatement pst = conn.prepareStatement(query);
pst.setString(1, pid);
pst.setString(2, fn );
pst.setString(3, ln );
pst.setString(4, add );
pst.setString(5, city );
pst.setString(6, phone );
pst.setString(7, mid );
pst.setString(8, mid );//this last two
pst.setString(9, pid);
pst.executeUpdate();
JOptionPane.showMessageDialog(null, "Patient Updated");
pst.close();
}catch(Exception ex){
ex.printStackTrace();
}