Beginner - Any swimming coaching available?

Have you looked into swim lessons at your local YMCA?  They are also on a schedule but I think you can join within the first couple of weeks of the session. I've also found that if you go to the pool at the Y on a slow day, the lifeguards will actually give you some pointers and watch you swim to see where you can improve. 

You could also Google LI triathlon clubs.  They typically provide swim training during the off season at a local pool.  

Hope this helps.