The most common funny sensation that can occur in the chest after a strong cough is something called a vasovagal reaction. Basically what happens in this setting is that the coughing stimulates nerve ending which temporarily cause the heart to slow down before speeding back up. This can create a very funny 'fluttering feeling' in the chest which should resolve within a few seconds after the coughing episode.
Similarly, a strong coughing episode may provoke a spasm in the muscles between the ribs, which might be felt like a strange 'fluttering' or 'cramping' sensation in the chest.
I would suggest that you talk to your primary care doctor
about this issue. I say this first because, although based on the examples I have given you, it is unlikely that this sensation is a related to a serious medical problem, it is impossible to rule out a more serious heart or lung cause without a full medical examination, which your doctor can do for you.
Also, if you are having as frequent episodes of strong coughing as it sounds like you are, then your asthma
is probably not well controlled, and you need to talk to your doctor about increasing or changing your asthma medications.