Unfortunately, it is difficult to find a place that rents ice axes. You can call Elevation in Lone Pine. Bishop is an hour's drive north, so probably not worth the extra distance, but try Eastside Sports. I'm pretty sure Elevation rents crampons.

I would go ahead and buy an ice axe; you can find them for $50-$60 on ebay.

Then, make sure you watch videos on the proper techniques and use, and once you are on the mountain, take some time to practice. Start by finding the links in this post: Links to important Whitney information