Get shoes that have a fairly flat outer sole that work well for you.
Buy some leather, nice and thick similar to this: http://www.tandyleather.com/en/product/economy-single-shoulders-tooling-leather or you can get sued like this: http://www.tandyleather.com/en/product/assorted-suede-splits-2
ideally, use a bench sander like this one: http://www.amazon.com/SKIL-3376-01-4-Inch-36-Inch-Sander/dp/B00J21SL4U/ref=sr_1_5?ie=UTF8&qid=1456411632&sr=8-5&keywords=sanding+station
To sand the soles flat. Take the leather and cut it out to be shaped almost the same (but maybe slightly larger) than your shoes then use some urethane rubber glue like this (note that if you use suede you'll probably want to use rubber cement): http://www.amazon.com/Gear-Aid-Freesole-Urethane-Repair/dp/B007UTZXT2/ref=sr_1_1?ie=UTF8&qid=1456411757&sr=8-1&keywords=gear+aid+freesole
Once the glue is dry use a box cutter to carefully pair the edges down so that they are flush to the sides of the shoes.
you now have a pair of shoes that don't cause you pain that can be used for dancing.
optionally, if you're not the do it yourself type, you can pay a cobbler to do the work. I expect it would cost between $30 and $60 to have a cobbler do it. Our local dance scene actually had someone who was a cobbler and would do it on the side for people for cheap.
Edit: I just remembered the exact rubber adhesive to use for dance shoes. It's called "barge" and you can get it here: http://www.amazon.com/Barge-All-Purpose-Cement-Rubber-leather/dp/B00B5XDPLC/ref=sr_1_5?ie=UTF8&qid=1456412085&sr=8-5&keywords=barge