It does sound very much like an allergy, a contact dermatitis due to some allergen that you came into contact with.In contact dermatitis, it is common enough not to be able to trace the source. Changes in detergents, etc. are the most common causes, but since this is ruled out, it could also be anything that you touch, like sme new cosmetic, gloves, etc. It could be from some new article of clothing or jewellery. They might also be due to some new medications that you are using.
It could also be due to some food that you took very recently. Watch out for foods like shell fish, sea fish, meats, cheese, etc. Also any new types of processed foods. If you do find anything which could be the cause, then try to avoid it. Link1. Link2
However, if new spots keep on appearing after you have tried this out for about 10 days, then you should approach your doctor and get it examined.
Next, you can take an anti-allergic tablet, an antihistamine. You can take Tab. Alavert 10 mg once daily (OTC). It will be more effective than Benadryl. Also, apply a soothing lotion like calamine lotion, also available OTC.
I hope this answer was helpful. If you need more information, feel free to ask. For accepting this answer, please click on the green 'accept' button below. Feedback/Bonus will be warmly appreciated.