I get eczema under my watch strap but nowhere else. Is it some sort of allergy?

If the watch strap is metal, you could be allergic to nickel and have
allergic contact eczema. This is different from irritant contact
eczema in several ways as it is a type of immune problem called a
delayed hypersensitivity reaction. The key points about it are:
• previous contact is necessary to induce the response;
• the response is specific to one substance;
• all areas of skin will react once sensitisation has taken
place;
• sensitisation persists indefinitely, and desensitisation is
unlikely to be possible.Various patterns are seen, depending on the original site of
contact. Your case is typical of nickel allergy, which can also be
seen under jewellery and metal fastenings in clothing, such as the
studs in jeans. Other patterns include fingertip eczema from garlic,
and eczema on the face and neck from perfume. An allergic cause
should be suspected if the pattern of eczema is unusual – eyelids,
around leg ulcers, hands or feet – if there is a known exposure to
some of the common allergens, or if the type of work is ‘high risk’,
for example hairdressing, nursing, gardening or floristry.