You have provided a very good description of your daughter’s illness. We should assume that the diagnoses of pneumonia and bronchitis were correct. It is also likely that she continues to have bronchitis and/or asthma, the asthma having been brought on by the infectious disease of her lungs. In this circumstance, the asthma may or may not persist on its own and the apparent response to ventolin is encouraging.
It is very unlikely that her lungs would have been permanently damaged, by either the infection (pneumonia) or by the antibiotic treatment. It is more likely that her current symptoms (cough and wheeze after running and playing) are caused by asthma and would respond to other asthma medication, in addition to the ventolin. Control of the asthma will most likely require additional asthma medication, taken regularly on a daily basis.
You should discuss what I have just discussed with her doctors, ask that they take the likelihood of asthma seriously and request that they provide further treatment. It would also be advisable for them to order another chest X-ray to be sure that the pneumonia has cleared.
Given what you have stated, “she is just fine, very energetic, great appetite (even as she is wheezing and coughing), drinks plenty of water, no temperature, nothing.” It is highly likely that the previous infection is cleared and that her current problem is asthma. Also very likely that she has healthy lungs, save for the asthma, and that she will respond favorably to good asthma therapy. Finally, you ask if, “her lungs just need some rest.” The answer to that question is definitely, no. She should be encouraged to be as physically active as she wants to be.
Good luck
Thank you so much for the response. This is exactly what I needed as just a couple of minutes ago I got her down for her nap after a crazy bout of wheezing. It feels as if its getting worse, or perhaps Im just getting more worried, but after reading your response I feel much better. Hopefully next week we will be able to go to the hospital where she was last treated (4 hours away) as we werent able to so far due to bad snowfall in the mountains which we have to cross to get there. I will mention this to them and hopefully we can get things rolling with some ashma medicine. My last and final question would be if it is possible for this asthma to clear up, I've read that in some cases with toddlers they grow out of it. Again, thank you for the quick response and the detailed answer.