Is it normal for allergy tests to give different answers (comparing blood vs. Skin)?

It can be. A blood allergy test measures ige response to allergens. These responses are graded from 0 to 6 where 0 is no reaction and 6 is maximum of ige to allergen. The skin test is where a small amount of allergen is injected into the skin and if there is 2mm swelling after 10 min. It's positive. The ige antibody levels in blood do not always correlate with the allergic reaction, so there can be a diff.