There are several different ways you can measure distance to an object using IR:

• Reflected light intensity: The easiest method is to send a beam of IR light and then measure how much IR light has reflected off the object. It only needs an IR emitter LED and an IR receiver. Think of it like pointing your TV remote at your ceiling and the signal gets reflected into your TV. The IR receiver will generally receive more IR light when the object is closer to it than when the object is far away, so this can be used as a simple way to measure distance. It's not perfect, some surfaces will reflect more light than others, such as shiny white objects compared to matte black objects, but it can be good enough for some purposes. This has traditionally been done using sensors by Sharp such as the GP2Y0A21YK at Sparkfun for $14, but they're somewhat expensive & large for a DIY finger-worn device affordable in the 3rd world. Luckily a custom sensor could potentially be much cheaper & smaller and with much faster response than the Sharp sensors.
• Projected light: To measure the distance to many points on an object at the same time, we can project narrow strips of IR light and see how the reflection is deformed from a nearby camera. This is the method used by some consumer motion tracking devices such as the Xbox Kinect and Intel RealSense, but is too complex & expensive for a DIY finger-worn device.
• Time Of Flight / LIDAR: We can send out a pulse of IR and measure the amount of time between sending the pulse & receiving it. Since we know the speed of light, we can calculate "distance = speed x time". This method is significantly more reliable & accurate & consistent, but unfortunately the equipment has been fairly large & expensive, such as the roughly $100,000 2D LIDAR sensor used on Google's self-driving car or the $150 LIDAR-Lite.

Comparing the 3 options above, a simple custom-made reflected light intensity sensor still seems like the best option for this project, since it should be small & cheap enough to have 2 or 3 of them on a person's hand and with almost-instant response, making it great for instant feedback, compared to the more complex devices mentioned above that only update around 30 times per second.