Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Delilah. I do have a few thoughts as to what might be going on with her since she's coughing again.
1. If she were exposed to a different viral or bacterial strain, then she could develop symptoms of kennel cough within a short period of time even though she developed this condition last month.
2. She could have ingested something very irritating to the back of her throat such as a stick or rawhide or something similar.
If that's the case, then a diet of softened kibble (soak it in water for 15-20 minutes) or canned food for a few days is recommended; the coughing/gagging should resolve within a short period of time.
3. Just because she had kennel cough last month (if the diagnosis was accurate) doesn't mean that other conditions wouldn't develop which sound similar. Bronchitis, collapsing trachea, cardiovascular problems, laryngeal paralysis...all are possible explanations for her behavior.
If this were my case and the problem didn't resolve on it's own within a few days and my physical exam was normal (no murmurs auscultated for example and clear lungs), then I might dispense antibiotics since many of the conditions mentioned in #3 also have a bacterial component to them.
Otherwise, I'd take a chest x-ray to evaluate the heart and lungs with a possible ultrasound as the next diagnostic step depending on the results.
I'm reluctant to suggest over the counter cough suppressants since if this is kennel cough, I want to inhibit removal of secretions. However, Benadryl (Diphenhydramine) may be helpful in drying up those secretions. The dose would be 1 mg per pound of body weight twice a day although sedation can be seen as a side effect.
I hope this helps and that she's feeling better soon. Deb