Your skin condition is like photosensitivity/ photoallergic reaction.
I think that because it appeared on your exposed part of body. Next but rare probability is polycythemia
rubra vera, a disease of blood cell where burning and itching of body increased after hot bath.
I like to suggest you to exclude 2nd one first by doing blood test
If your blood report will normal then take antihistamin tablet e.g. ATARAX
25mg twice daily for a week
and apply a sunscreen cream/ lotion every morning [Spectraban]
Consult us after one week.