Unfortunately some kits come with a basic Bobbin and sometimes the Bobbin will have a bur or a rough edge that causes the thread to frey as well, I second the earlier thoughts about the 6/0 or 8/0 and perhaps a new Bobbin or maybe upgrade to a ceramic Bobbin/ceramic with a ruby tip. I also second the lessons idea, books, magazines, this board has some awesome information, the expo this weekend and the web. I have learnt so much by watching others tie, especially Mr. Leroy Hyatt from Fly Tying the Angler's Art.
Good on yah for tying your own flies:)