Not to be gross but I can tell you I had similar rashes on my arms and chest after my first visit to Belize (Hopkins) last November. My doctor diagnosed it as eczema and gave me a prescription called Prednizone. That helped temporarily but as soon as I ran out it came back in force. To this day I still have traces of it.
Another possibility is ringworm, we played a lot with the dogs on the resort and they can be carriers of ringworm. A friend of mine who had ringworm years ago said her rashes looked exactly the same. Run these by your doctor, maybe he can test for them. Good luck.