If it's a sentence, you shouldn't put the words into a doubly linked list
If you're counting occurrences of a word, I would probably just do something like this:
public int CountWord(string sentence, string word, bool caseSensitive)
{
int count = 0;
string[] parts = sentence.Split(' ');
if (!caseSensitive)
{
word = word.ToUpper();
}
foreach(string part in parts)
{
if (!caseSensitive)
{
part = part.ToUpper();
}
count += (part == word) ? 1 : 0;
}
return count;
}