Thank you for your question.
You certainly seem to have developed an allergy, but it might be to anyone of the ingredients in the products you used, rather than aloe vera itself. These products contain many ingredients; and allergies are common to things such as preservatives and perfumes. Typically you won't be get affected at the first time you used a product, but that’s when the sensitisation occurs. When you come into contact with the substance you have become sensitised to on a second occasion, that’s when the allergic response occurs. You can check for yourself that youhave ever reacted to something else that might contain the same ingredient such as another cream, elastoplast, a perfume etc.
You should avoid this product in the future as it will always cause an allergic response. For now, just let your face settle down naturally. You could take an antihistamine to help if you wish.