I have a couple of thoughts about this.
One is that eating disrupts a person's normal breathing pattern and can trigger asthma. You may want to take 2 puffs of what you call your "emergency" inhaler (probably albuterol or similar) about 10-15 minutes before eating, so that you can prevent the coughing. If you still cough, you could still take a couple of puffs of the "emergency" inhaler to stop or reduce it.
Two is that if you were just diagnosed with asthma, it sounds like it is not under control yet. When you go back for your check with your asthma specialist (which should be pretty soon since you're newly diagnosed), please discuss this with him/her. If it's still happening by the time of your check up, your doctor may have to increase your asthma controller meds until your asthma is under good control.
Three is, are you absolutely positively 100% sure that you do not have acid reflux? (Some acid reflux is silent, in that it does not cause heartburn symptoms.) Because this also sounds like acid reflux that is irritating your lungs so much you have an asthma attack.
Asthma tends to go hand in hand with acid reflux because of two things: long-acting bronchodilators tend to loosen the lower esophageal sphincter (which prevents acid from coming up into the esophagus), and coughing tends to increase chest pressure and promote reflux. Discuss with your doctor whether you should take an acid reflux med to address this. Even something like Tums would help after eating.
So, to sum up: try using 2 puffs of your "emergency" inhaler 10-15 minutes before eating; use the "emergency" inhaler to stop coughing; and think about eating a few Tums after your meal to reduce acid. And definitely discuss this with your doctor at your early convenience.
Hope some of this helps you - take care & good luck. Judy