Hello,
These symptoms can be due to cholinergic urticaria. It is a form of chronic hives that is caused by an increase in body temperature but can be idiopathic also. Take some antihistaminic like Benadryl or Claritin and apply some calamine lotion on the hives. If the symptoms persist then please get it examined from a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
I am not a doctor, so you might want to see one, but here are a few thoughts.
1 Where you live now is warmer and less humid, so dryness issues arise in my mind. Your skin may be too dry.
2 Alternatively when you eat something hot the blood goes to those areas, thus you feel hot.
3 The other thing could be about circulation, or should I say lack there of. But I am included to think it is #2, above. or a combination of 2 and 3 where you might have some circulation blockage issues and the exercise helps, in addition when you start sweating the problem goes away.
See what happens over another week or so and if nothing gets better you probably could go see a doctor and see what they say. If it is circulation related you should probably address that, and doing exercise is a great way to get the blood moving.
Do you have any issues with this when you eat?