My Lyme symptoms started in 2009 and came and went for years. In April, 2015, I got sick with bronchitis and out of control inflammation. Within 10 days the inflammation started causing pleuritic type chest pain and snowballed from there with asthma-like symptoms that included shortness of breath, feeling like I couldn't expand my lungs and get a satisfying breath, tightness in my chest and across my ribs, stiffness in my chest wall, and sometimes a mild unexplained cough.
Two months later, I went to a pulmonologist and had a chest X-ray, pulmonary function test (PFT), and a methacholine challenge test for asthma. The tests were all normal and I was negative for asthma. Doctor gave me a Rx to take double the regular dose of a potent steroid inhaler usually prescribed for asthma. It got me to about 90%. Symptoms starting coming back a month later.
This was all before I knew about Lyme.
The methacholine challenge test is the only proper and definitive way to diagnosis or eliminate asthma. Please get the pulmonology work up to be sure.