There is a word counter one Nanowrimo, you don't have to count it yourself. and just to check on it I usually use www.wordcounttool.com it works great.
I don't have microsoft word either, and it sucks. Why don't you try Abiword? I found it online and it's a free word processor that you can download. It's sort of ghetto, but it works and it can count your words for you. :)