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It's a normal reaction to emotional upset. It has no particular clinical significance. We often describe emotional upset and rejection as having a "broken heart." Of course, the heart isn't really broken, we just feel that it is.
It's just a feeling because of your emotional upset. Some people actually describe pain. Some have a hot feeling. You feel cold. It's not exactly psychosomatic, but it is harmless. Perhaps your brain associates the rejection with coldness. There is no specific physiological reason for it.
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