I was afraid of air pollution in Barcelona too as my wife is allergic to some pollutants but if you don't take a flat facing the street and go slightly uphill (gracia, sant gervasi, sarria, ...) it is totally fine. She hasn't had any problems.

Barcelona used to be much more polluted but from what I am told they made a major effort to clean up around 2012. https://air.plumelabs.com/en/year/barcelona