How does the brain project pain on to a particular part of the body? How does our brain translate periheral sensations due to injuries into pain perceptions? As an in silico analogy - if a stimulus is applied to a sensor it can be transmitted to a microprocessor. The micro processor then processes the information. However, a microprocessor will not cause the sensor to "feel" that stimulus. In other words, the processed information of the sensor is not projected back to that sensor as a perceived stimulus. Hence, in electronic circuits the information is processed unidirectionally. In contrast, in the peripheral nervous system sensory inputs are processed in the central nervous system, ultimately resulting in perceived sensations on the location of the sensor. Thus, apparently, the peripheral and central nervous systems operate in a feedback loop. 

How does our nervous system do this? In other words, how does it localize the source of the stimulus (e.g., pain) and turn that sensation into a perception on that location, rather than just unidirectionally process the information?
Short answer
Peripheral sensory information is projected unidirectionally to the brain. A sensory strip of the brain contains a topographical representation of the surface of the body that facilitates the localization of peripheral stimuli. Hence, there is no feedback from the brain to the periphery necessary to locate the source of a peripheral stimulus.

Background
The sensory systems in the skin project unidirectionally to the somatosensory cortex. In the somatosensory cortex there are so-called topographical maps. These maps contain the neurons that connect to different parts of the body. Typically, neurons receiving information from one part of the body are clustered together in the brain. For example, the sensory outputs of the peripheral touch receptors in the finger digits ultimately synapse onto cortical sensory neurons that are close together. Touch receptors in the toes for example are processed farther away (Purves et al, 2001). A famous graphical presentation is the somatosensory homunculus (Fig. 1), showing the areas of the sensory cortex devoted to processing sensory inputs in different bodily parts, including touch; 


Fig. 1. Sensory homunculus. source: Russel &amp; Dewy (2007) 

The sensory cortex, hence, is a highly structured cortical area, in which sensory information (including outputs from touch, pain, heat and cold receptors for example) is funelled to a topographical representation in the brain. See for a nice introductory this video from Khan Academy. 

To answer your question - there is no feedback from the brain back to the periphery necessary to process peripheral sensations into localized perceptions. The bodily map is maintained in the brain and contains all the information necessary to pinpoint the stimulus locus on the skin. This localization is more accurate when more peripheral fibers are present, i.e. when receptor density is higher. This is centrally reflected in the sensory strip in a larger area of the cortex being devoted to bodily parts with denser receptor innervation. This is the reason why the homunculus is so distorted (Fig. 2). For example, the lips, tongue and finger tips are highly sensitive and contain high densities of peripheral receptors. In effect, relatively large areas of the somatosensory cortex are dedicated to processing their inputs.  


Fig. 2. 3D representation of the sensory homunculus. source: University of Calgary   

Reference
- Purves et al., Neuroscience. 2nd ed. Sunderland (MA): Sinauer Associates (2001)
- Russel &amp; Dewey, Psychology: An Introduction (2007-2014)