Thanks for posting your query.
You may have possibility of COPD
(allergic to cat fur).
You should go for spirometry
or pulmonary function test.
Improvement in FEV 1 > 20% after bronchdilator therapy suggest asthma and less than 20% suggest COPD.
You can use mask and anti-allergic medications for control of allergy
Dr. Mayank Bhargava