There could be many chemical allergy possibilities. A chemical used in manufacturing the toy or a product you have used to clean the toy that has left some residue. It could also be coinsidental. Many people have delayed alelrgic reactions. If this is the case, finding the allergen will be much harder.
Allergies develop or can worsen at any time. I would recommend that you put the toys she has reacted to up for a while at least until you see the dr. You may need to keep an Epi-pen handy just in case.
Praying that your dr is able to provide answers and help.
Hi, welcome to the forum, her symptoms are suggestive of Contact dermatitis. Usually allergens are small molecules which can penetrate the layers of the skin and cause the allergic manifestations. Plastic allergy can be possibility but uncommon.
Other common allergens are Jewelry and clothing snaps containing nickel, soaps, cosmetics, moisturizers etc.
Topical lotions such as calamine decreases pain and pruritus. Systemic antihistamines (antipruritics) such as hydroxyzine or cetirizine against prescription may be helpful. Even addition of corticosteroids has possible benefits. The actual management would be avoidance of the primary allergen.
I suggest you to consult allergic specialist for her further evaluation and treatment. Take care and regards.