That sounds like a problem that could become very annoying over time, and could be a sign of other issues that are occurring. There are a few questions that I would ask before we can tell for sure, but I would wonder what medical conditions you have, what your heart medication is (and why you take it), what your weight is, if you have any symptoms of heartburn, and if you have any family history of any medical conditions that might be relevant. Coughing after finishing a meal could mean different things depending on how much you are coughing: if it is just a small cough to clear your throat, it would be less of an issue than a long bout of coughing, or a fit.
In general, one of the first things that I would think about (assuming that all of the answers to the above questions were as expected) would be acid reflux
, also known as GERD, which is very prevalent in overweight people especially (with 60% of Americans being overweight, of course). The constant acid coming up from the stomach causes irritation that induces the formation of mucous, that you are then constantly trying to clear by coughing. Your symptoms sound somewhat typical from the little bit you have described. Please see your doctor
to make sure that nothing more serious is occurring, and to discuss treatment options and a possible painless procedure that would allow visualization of your throat.