Reseach on feeling pain of other people
I believe what you are referring to is called 'sympathetic pain,'and the reason you can't find any papers on the subject is because it is not really a well studied concept. That is primarily due to the lack of robustness in the sensation and idiosyncratic nature of the phenomenon. Personally, I'm not too familiar with the concept beyond placebo treatment of patients with such pains.

HOWEVER, I will explain the different types of pains briefly, their biology, and where the pain you have described fits roughly. There are three categories of pain (scientists sometimes argue four, but for our sake let's say three): nociceptive, inflammatory, and neuropathic. Nociceptive pain is the immediate pain reaction you get when you sense something harmful. It's that jerking sensation you get when you touch something hot or you feel something hazardous coming your way. This pain comes from peripheral nerves that link your senses of touch or perception directly to your spinal chord for an immediate knee jerk reaction. Thus, there is no central nervous system (or brain) processing of the pain, just a reaction. You end up feeling the pain more intensely later once the moment has passed. Then inflammatory pain is the pain you get when you cut or bruise yourself, have allergies, stuffy nose, etc. It is the more common and treatable types of pain and is easy to detect. It comes with redness, swelling, and sensitivity to the general area. Biologically your body is stimulating this pain because your inflammatory system is trying to attack any invasive particles or repair damaged sections of the body. There has been much research done in this type of pain (see sources) and is treatable with non-steroidal anti inflammatory drugs (NSAIDs) such as aspirin, Tylenol, etc.

The last type of pain, which is the sympathetic pain falls into, is called neuropathic pain. This pain is more abstract and is often described as constant and idiosyncratic (non standard intervals). In research it is often modeled by inducing diabetes and doing damage to the nerves to cause constant pain signals to the brain. However, the method is controversial in both practice and in efficiency of modeling. This because there are often many different biological ways to induce cognitive pain and it is primarily central nervous system based (aka in the brain), whereas this type of pain is specifically induced by nerve damage (hence neuropathic). This type of pain is often tested using cognitive based test parameters to see if a drug can relieve some of the mental struggles either caused by the pain or causing the pain. There are also such cells called "mirror neurons" that fire when you sense (visual, audio, touch) something and then cause a similar behavior or sensation to occur within the person. It is possible that seeing or feeling someone else's pain causes these mirror neurons to fire for certain people, perhaps due to associate learning or a memory that person has that reminds them of pain they once had. I've attached some literature on the subject for your leisure, but it is a poorly understood science that we are trying to grasp in modern research. Hopefully that answered your question!

Sources


The Principles of Neuroscience by: Kandel, Schwartz, Jessel, Siegelbaum, and Hudspeth (most indepth source)
Pyschopharmacology by Meyer and Quezer
From Mice to Men: Jacqueline Crawley
Pathology Based Pain
Inflammatory Pain Review
Neuropathic Pain Review
Mirror Neurons