It is hard to say what the white spots, all over the arms and back, are without seeing them.
Fungal skin infection is a possibility considering that swim in pools. It is easily diagnosed by taking a swab from the affected place on the skin for microscopic examination. The fungal skin infections differ in appearance depending on the type of the fungus that caused them. In many cases, changes in skin pigmentation might be present.
The skin changes are associated with edges that are more red (because of inflammation) than the surrounding skin. Itching might be present, too.
The white spots might be due to pigmentation problems. One suggested condition is vitiligo. Vitiligo is a chronic disorder that causes dispigmentation in patches of skin.
Skin patches might become more visible after sun tanning, because melanin (the skin pigment) is not produced enough in the affected skin patch.
You might want to visit a dermatologist where adequate treatment might be recommended. Exposure to UVB narrowband light is one of the treatment options that might significantly help you. Just consult with a dermatologist.
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