Whenever any doc offer me a prescription, I immediately ask for the names of the drugs in it and if there is a generic equivalent. Sometimes, with combo drugs, I might have to take 2 pills or use 2 inhalers, but the inconvenience can be a small price to pay for saving a lot.

Generics do not always work for everyone - sometimes the filler or propellant may be different between the name brand and the generic, and cause issues for a few sensitive individuals. I have had that experience with 2-3 medications in my lifetime. But it is definitely worth a try.

Also, generics are not yet available for many new drugs - these are protected by patent for a number of years, to allow the developing company to recoup their enormous research and development, testing and marketing costs before they have competition. For example, most biologics are still under patent protection.

Here's a cautionary tale for you on why slowing progression is important! As the mother and aunt to at least a dozen asthmatic kids, and an allergy sufferer, I should have known better, but I "pretended" not to have asthma for years, refusing to use albuterol because it made my essential tremor worse.
Then I started to have regular exacerbations, with frequent bronchitis. I still resisted using a nebulizer and tried to rely on my Levalbuterol rescue inhaler. Over 30 years later, I became a walking case of repeated asthma attacks, bronchitis and pneumonia, being treated several times a year with oral steroids and antibiotics, "getting better" only to relapse in 6 weeks or 3 months.
Finally, I was diagnosed with Bronchiectasis and two lung infections. Now I have to be eternally vigilant to keep infections away and do daily airway clearance to remove the mucus my lungs can no longer expel on their own.
Please listen to your pulmonologist so you don't end up as an old lady with Bronchiectasis, COPD or another complication.