Tink has indeed always been there, and was certainly not given her name until she was animated! In the original manuscript of the play, she was a fairy called Tippy or Tippytoe but by the time the play was first performed in 1904, she was definitely Tinker Bell (Tink for short), an ordinary fairy tinker who mended pots & pans. Barrie did make changes to the play but Tink always featured, although not in any human form: she was "played" by a darting light and "voiced" by ringing bells. The final version of the play as written by Barrie was published in 1928. Tink also featured in the novel published in 1911, and in some of the early illustrated editions of the novel, not just as a dancing light.
I don't know where you're based, but copies of the novel are quite easy to find in the UK and US (and other English-speaking countries) as the original work has been reprinted many times over the years by all major publishers - although make sure it's the unabridged version by Barrie, not the abridged version by May Byron, or adapted by Daniel O'Connor (and others). You can also find it as an ebook on Project Gutenberg (http://www.gutenberg.org/ebooks/16) and on this site in the database.
As for the play, again, depending on where you live: the play is still in copyright in the US but copies of editions published in the 30s and 40s can be bought on sites such as eBay or Abebook (look out for 'Uniform edition of the play' published by Scribner's in the US or Hodder & Stoughton in the UK). Sometimes used copies of the acting script published by Samuel French can also surface on eBay.
Hope this helps!