Does having a positive skin test to a food means that I am allergic to that food?

No. We need to consider several values of the skin test, such as its specificity, sensitivity, positive predictive value, and negative predictive value. Think about this: if 100 healthy people (no food allergies) are skin tested to peanuts, some of them will come out positive even though they eat peanuts without problems. The oppositive is true if we test 100 peanut allergic people; some of them will be negative in the test. This is why the diagnosis of food allergy needs to be strongly supported by a clear history of reactions to a certain food and positive tests (skin tests, blood test, elimination tests, challenge tests, an others).