Am I allergic to tree nuts?

Ever since I was little I've had these reactions to tree nuts. The symptoms include: Throwing up, scratchy/closed up throat, and I get really hot. But one time I ate a candy bar that I didn't know had almonds in it and nothing happened. But they were small, so that's why I didn't notice them. Then I found out later that my dad knew but didn't tell me, just to test it. My dad says it's all in my head, and someone told me that getting sick isn't an allergic reaction. So, am I right about being allergic?