What is the disgnosis and medication cost for cat potentially with asthma

Anybody been thru the process before and know what the approximate costs and details are about getting a cat seen for potential asthma?

She has a really jerky/compressed in/out breath that makes her stomach look hiccupy and she often has several fits of dry heaving all day. She used to throw up constantly but not so much anymore but she still has her training to jump of the couch whenever that arises.

Thanks 🐱