Unfortunately, there is no easy way of checking. That is the nature of research; you have to go through all the relevant material and determine if your idea has been done and if so can you still add to that topic. Also, it is possible that your project has not been published as a PhD thesis yet, but that someone is currently working on it and will finish before you. Depending on your field, you would then have to rework your material so that it remained a considerable contribution.
I'm sorry that you have resource constraints, but I imagine it would be very difficult to do in depth research if you can't access relevant journals? Or do you mean you will have access provided you begin a PhD? At this point I would go with your project and if it turns out later that someone has done it you can amend your proposal. Good luck :)