Yes, the symptoms show that you are allergic to perfumes. Perfumes contain various types of chemicals, which can cause or initiate allergic reactions in sensitive people. It is very difficult to identify that allergy is because of one chemical or combination of chemicals. These allergic reactions may include headache, breathing problems and skin rashes also.
You definitely need to avoid wearing the perfumes or fragrances. You also need to be cautious while using other personal care products and household products as they might contain perfumes or fragrances. If you are sensitive, it is very risky while going out for a party or a function.
You can consult a doctor, who may help in identifying the factors. They can also tell you how to lessen the symptoms and avoid the possible exposure to the product.