From the symptoms you have described, it is most likely that the infection you had has created some degree of postnasal drip. This is drainage from the nose and sinuses dripping down the back of the throat. There could be several reasons for this drainage. One reason is an allergy. A second reason is a non-allergic, non-infectious inflammation in the sinuses that could be lingering after your recent cold. A third reason is chronic sinusitis. Postnasal drip can cause coughing to the point of vomiting and shortness of breath as a result of irritation of the throat and lungs. You may experience the postnasal drip as a constant feeling of mucus at the back of your throat. Typically this is worse at night when you lay down to sleep. Generally this irritation feels the worst when you wake up and gets better as the day goes on.
The fat content in dairy products can thicken mucus. Generally eating dairy products with less fat content is helpful. Drinking plenty of water will help to thin the mucus so that it moves more easily. As long as you are not on a fluid restriction you should be drinking 6 to 8 8-ounce glasses of non-caffeine non-alcoholic fluid daily. Clearing your throat can irritate your throat and make it sore. When you feel the need to clear your throat sip some water to clear the mucus.
An antihistamine can dry up the postnasal drip. However, it may make the mucus thicker and more difficult to move. A decongestant like Sudafed
I have exactly the same problem. I went to the doctor, I have polent/mold induced asthma, and she throught that was the problem. I have been using Albuterol for this. In the last three days since seeing the doc it has not gotten better. I wake up every 3 hours or so coughing. I had a cold two or three weeks ago and this is all that is left. I am swore like I have a cold. I cough up clear/white mucus so it's not an infection. The cough is now bad when I wake up and go to sleep. The area around my ribs hurt from coughing. Can anyone help? I am going back to the doc sometime this week.
You wrote: "Sometimes it occurs after eating a meal. The cough becomes very severe and I feel shortness of breath. Additionally, I often vomit when this happens."
Have you been tested with a "ph probe" in your esophagus, to see if you might have a high up (intermittent) type of gastric reflux, called LPR (laryngo pharyngeal reflux)? Have you had a laryngoscopy done, to see if there are any physical signs of LPR? (such as redness in throat or in vocal cords, swelling of vocal cords, excessive mucus in vocal cord area)?
You may want to ask your primary care doctor if a referral to an ENT/ear, nose & throat specialist, and to a gastroenterologist, and to a pulmonologist (lung specialist) might be helpful, for getting fully and accurately diagnosed.
Good luck in getting diagnosed and treated. Hope you feel better soon.