Making words for a new language of your own isn't as scary as it seems. Tolkien was a language expert so it might never be as complex as his, but the basics of what he did was to look at existing and ancient words and create new words from roots. Also he would 'retrieve' an old word and give it new/alternate meaning - e.g. how Ent, Old English for Giant was used.
The difference might be that while Tolkien created the story so he could use his invented languages, you might be inventing a language to fit the tale; not all that difficult if you do it while you are writing, and of course we have the benefit of computers for handy cross-referencing.
It might be worth having a look at some other books where writers have created new words, e.g. 1984 and A Clockwork Orange.