You might want to talk this over with your pcp (primary care physician) and maybe get him to set up a lung function test. How often do you feel you're short of breath and are there any specific times? You might want to jot down on paper your next shortness of breath and take it with you to the doctor!!!
Otherwise you might always be wondering. For your sake I really and truly hope it's not asthma.
I would not wish what I'm going through right now on anyone. I've had asthma all my life.
Take care and best wishes.
p.s. I wish you well with the LYME