Does this sound like asthma? I really need some insight!

Way to go on not smoking.  With your history of bronchitis don't ever smoke, not even one. 

?I'm not a doctor and even a doctor could not properly diagnose and treat asthma over the internet so you do need to go back to the doctor.  I have had asthma since early childhood and at near 50 it has not stopped me from participating in sports, running several marathons, triathlons, hiking, traveling and leading an active lifestyle.

?For me the main cause was and is allergic, however bronchitis was also a factor especially when young. I also get something called EIA (Exercised Induced Asthma) which is quite common also with elite athletes (many olypmic medal swimmers get this).  EIA is the easiest to spot and deal with but surprisingly in my experience surprisingly many random GP doctors did not know much about it (at least 15 years ago).  It tends to happen in cold or dry air although a bad pollen day will be an aggravating factor.  Most often right at the beginning of exercise or during a spike of effort.  The prevention is one puff of albuterol 5 or 10 minutes before the start and then do a good 15 minute warmup.  Once i am hot and going full pace after 15 minutes it's very unlikely to happen.  If I get it near the start I slow down a bit and wears off after about 15 minutes.  Usually i don't need to stop, but there is not need to push it - 5 minutes of walking also helps.  Listen to your body.

?As you have probably figured out I am thinking you might have EIA connected to some seasonal allergy especially since you mention a cough at season change.  Do you live in an area where many people suffer from pollen/trees/grass allergies? Or did you move within the last 3 years?

?The only thing that I don't get is the climbing stairs, unless it is ten flights in the cold.  Usually EIA is outdoors, you can read up on the causes.  Unless you were already getting a bout of asthma from allergies and all that did was let you know.

?The main and most obvious symptom of asthma attack is wheezing.  If you are having a reasonably strong attack you or someone else can hear it when you take deep breaths, although I read that it's more likely audible with children than adults.  Or when you breathe out hard you can hear and feel a wheezy feeling at the end of the breath, kind of like an accordian.  If you aren't sure of that symptom, your doctor should give you a peak flow meter or you can pick one up at the pharmacy without prescription for a few dollars.  You should take a baseline daily when you are clear to learn your peak flow, then when you have one of these attacks try it and see if there is a significant drop. Take your log back to the doctor, that can confirm it for them.

?I've never heard of ultrasound for asthma i doubt they could image the bronchial tubes to that detail, so if they are prescribing that they think you have something else that could be contributing.

?Bottom line: Have a positive attitude and remain calm.  It's not a death sentence! If you have it, it sounds to me pretty mild. It's easily treated and managed you just need to get on top of it and learn the triggers.  My personal experience is that asthma is like a fingerprint - the exact triggers and evolution is unique to every individual.  If you listen to your body you will be your best advocate.  And the fingerprint will change over your life.  I've been clear 5 years and now I'm having a little comeback during a particularly horrendous pollen season (everyone is suffering). I'll get on top of it and back to normal.