Viral infections like a cold can cause inflammation of the airways of the lungs. This inflammation can cause coughing. If a virus were the cause neither of the antibiotics you took would be effective in getting rid of the infection.
After the cold is gone, it is possible for the inflammation to linger. This inflammation can last for several weeks. Sometimes this inflammation may linger for 3 to 6 months. This inflammation may be the cause of the pain and irritation of your throat and upper lungs as well as the slightly constricting and burning feeling in your upper throat, lower nasal passages, and upper lungs. Eventually the inflammation will go away, and then your symptoms will stop. This is called reactive airways disease (RAD) and behaves a lot like asthma. On a simple breathing test, called spirometry, this may not show up. This inflammation often clears more quickly when it is treated with an inhaled steroid medicine, which is given to treat asthma. Usually this medicine does not help after just one use. It may need to be used every day for several weeks to months for it to help. Your doctor is the best judge of this.
Thrush is an over growth of a yeast that is normally found in the mouth, called Candida albicans. This causes a white discoloration of the tongue and mouth that generally looks like cheese curds. When the white patches are wiped off, the area bleeds and feels very sore.
Maybe a URI [upper respiratory infection] due to a virus.
You can have just some of the symptoms and still have it.
http://www.njc.org/medfacts/uri.html
UPPER RESPIRATORY INFECTIONS (COLDS) and ACUTE BRONCHITIS