An O(n^2) solution is incorrect. Try separating the string by letters.

The most efficient solution for this problem involves counting the occurrence of each letter and then iterating through the string again to search for the first character with a count of 1.

firstUniqueCharacter(String input)
   int[] count = new int[26];
   // Convert to lower case for easier processing
   input = input.toLowerCase();

    for (i = 0; i < input.length(); i++)
       // Typecast to int to obtain ASCII value in some languages
       if (count[input.charAt(i) - 'a'] == null)
          count[input.charAt(i) - 'a'] = 1;
       else
          count[input.charAt(i) - 'a']++;

    for (i = 0; i < input.length(); i++)
       if (count[input.charAt(i) - 'a'] == 1)
          return input.charAt(i);

    return null;