The good news is it sounds like you have identified the cause. How attached are you to those new shoes? If you noticed the pain develop after you bought the shoes, they are, at the very least, a contributing factor. Even though your toes have curled in for as long as you can remember they are still part of the problem. In many cases, it's the combination of shoe pressure on contracted or curled toes that puts abnormal pressure in between the toes. To treat this, you need to keep the pressure off of the toes. This means wider shoes to decrease the pressure on the 4th and 5th toes, and a pad between the toes, to keep the 4th and 5th toes from pressing against each other.
Toe separators can be found at the drug store, or
online. There are products which are labeled "toe separators" and they can be foam, felt or a combination of both. (don't purchase "medicated" pads for in between the toe problems) The padding goes in between the toes. If you continue to wear the same narrow shoes, but wear a toe separator, the pressure will switch to the outside of the little toe, so making changes in the shoes is important. Once changes in shoes have been made and the corn has resolved, you usually don't have to wear the toe separator anymore.
If the corn persists beyond 4 weeks after trying these treatments, I would recommend an appointment with a podiatrist.
The image below shows a larger foam toe separator between the big toe and 2nd toe, but the separators come in different sizes and can be used in between any of the toes.