Problem with boolean variable in email validation program

I am trying to create an email validation program without using the regex library. In one of my functions, I want to return a Boolean to check if there is an @ sign in the email address and also if it is in a valid position (the @ sign cannot be one of the first three characters of the string). However I am having problems with it because every time I run the program by entering in an email address with the @ sign in an invalid position, it keeps telling me that the email is valid. Please help!

valid = checkEmail(email); //function call 

if(valid == true)
  cout << "Your email is valid!" << endl;

else
  cout << "Your email is invalid!" << endl;


bool checkEmail(string email)
{
  int counter;
  int length;
  bool firstThree; //checks to make sure @ is not in the first three chars

  counter = 0;
  length = email.length();
  firstThree = false;

  for(int i = 0; i < length; i++)
  {
    if(email[i] == '@')
      counter++;
  }

 for(int y = 0; y < length; y++)
 {
   if(email[0] == '@' || email[1] == '@' || email[2] == '@')
      firstThree = true;

   else
       firstThree = false;

 }

 cout << "\n" << counter << endl; //check to see if counter works

 if(counter != 1 && firstThree == true)
   return false;

 else
   return true;
}