Is Twitter truly relevant to a new author?

With the publication of my new book, 'Windows to Other Worlds: Essays, Short Stories and One Novella' (http://www.amazon.com/dp/B00AZBO7NA), I have of course been researching marketing techniques for ebooks and the like. Facebook, Goodreads and Twitter seem to be the biggies for getting word out, however, I'm unsure of how effective Twitter is.  I haven't tweeted in quite a while, over a year, and so returned to the world of tweeting as a way of promoting my book. It seems to me that this cannot be a very effective tool. I don't have very many followers which would seem a detriment to my intention, but even with so few followers (only 28) and not many more that I follow (81) the tweets just whiz by and I have to scroll maniacally just to find anything amongst even those few folks whose tweets show on my wall.  How then can this be an effective marketing tool.  If someone who is following me has even just the limited amount of followers that I have, how can they weed out just that one post of mine which will lead them to my book. Is someone really going to pick out my tweet with the link to my book when it's surrounded by a flock of tweets by the likes of Barack Obama, William Shatner, Stan Lee and whoever is the Tweetmaster du jour?  I'm not sure that this avenue is even worth my effort.