Is "allergy" another word for pollution?

No: An allergy is an over exuberant immune response to a substance the body finds foreign in a smaller subset of people. These substances are usually proteins such as bee venom, food proteins, pollens, etc. Pollution is usually reserved for particulate matter from smoke stacks, gases like ozone, nitrogen and sulfur dioxide, etc. These gases and particles affect everyone!

Talking air quality?: No, they are very different. However, they both apply to atmospheric conditions. Finding out what pollens you are allergic to, and knowing what pollen is in the air (requires hand counting - such as done in my office) will answer what allergies are bothing you. But air pollution compounds the issue, worsening allergies and asthma. Both are important.