There are many people complaining about the same thing right now. It seems that "heat allergies " are on the rise.
My mom also suffers from this. We are in Canada, so we have lots of cold weather. She finds that wearing a vest, and not a full sleeve jacket helps her. She is cold, but she says it is better than what happens when she gets hot.
I would ask your doctor to send you to an allergist. They might have better ideas to help you.
Are you able to see a doctor who specializes in allergies?
You can also post this on the Alternative Medicines Forum, they know much about non prescription remedies that may help.
I just found this on the Neurology forum and it may help:
brachioradial pruritus.
Look that up and see if it fits in with what you are experiencing.
It seems Ketotifen gave good results! Two times a day for one pill.