I had bronchitis 2 months ago. Cough is better but still have an episode or two daily of short breath and crackling lungs when breathing...Normal?

Recovery. Any upper respiratory or lower respiratory infection can cause a prolonged and delayed recovery phase. During this time, it's not unlikely that you might have some periodic mucus or bronchospasm which causes the symptoms you describe. If you haven't done so recently, you need to see md to check you out and possibly do x-ray , etc.
Crackling lungs. This is not normal. Perhaps you had a bout of walking pneumonia or the bronchitis is not cleared. Check with your doctor to see why you are not getting completely well.