I know what you are talking about. Keep an eye out for shingles, just in case. This sounds more like nerve pain in the skin. I don't know if weight is an issue - I am very overweight, but had this way back wehn I was very underweight. The last few years there are days I cannot even stand clothing. Seriously, I fight to not cry from having very loose, light dresses that barely touch me because everywhere they touch the skin screams in pain.
If this doesn't stop, you may need to explore taking Lyrica or neurontin. Neurontin is the old version of the same medication. Both seem to really help nerve pain. Lyrica is approved for fibromyalgia and nerve pain and for several years was a big help to me. Lyrica supposedly has fewer side effects, but I don't know if this is true or what I was told at some point.
One cause for nerve pain is diabetes. Do you know if you have diabetes or are at risk for it? If you have not had this test, have your doctor run the A1C test which will tell you if you are at risk to develop diabetes. An early diagnosis is crucial for diabetes, so if there are any questions about if you could have it, get tested.
I hope it goes away for you.