Does pulmonary fibrosis cause my lungs to thicken?

Yes. Pulmonary fibrosis causes the inner latticework of the lungs to thicken. Given that this latticework supports oxygen and carbon dioxide exchange, and that exchange is dependent on the thinness of the transport membrane, pulmonary fibrosis makes the lungs work less efficiently, leading to shortness of breath.
Yes. The interface between alveoli and blood vessels will thicken oxygen has a difficult time to cross from air to blood fibrosis is a medical word for increased scar tissue.
Yes. Pulmonary fibrosis causes the thin membranes (alveoli walls) the scar and become thicker resulting in impared gas exchange (lower oxygen ) and shortness of breath.