By definition, acute cough is one lasting <3 weeks, sub-acute cough lasts 3-8 weeks, and chronic cough lasts >8 weeks [8]. Most acute coughs raise minimal concerns among health practitioners as they are generally caused by URTIs, usually have a short duration, and are self-limited.
Healing is a complicated procedure after tooth extraction. It may take from 3 to 5 weeks in normal person but it will take longer in diabetic patient, presence of infection after extraction, malnutrition, complicated surgical extraction, and smoking. Complete healing with bone deposition and remodeling will take from 3 to 6 months.
Two weeks is still very soon for all being removed, especially if you had all your teeth extracted. That's a lot on bones, gums etc. It can take up to a month for all wounds to heal. Continue following the dentist's instructions and taking good care of your gums. If you suspect an infection, go in as soon as possible.