I had a cold that started out with a sore throat then i got rid of the sore throat after four days now i'm stuck with endless coughing and sneezing?

It could be: allergy or cough variant asthma .or post nasal drip or bronchitis or pneumonia. See your doctor and get some medication.

See below: It's not unusual for a viral upper respiratory infection(cold) to settle in the chest(bronchitis) The cough can last several weeks slowly improving. OTC cough meds usually contain Dextromethorphan (DM) which may or may not help the cough. See a physician if you are having fever, shortness of breath, wheezing, pain on breathing or not improving over next 7 days. Sneezing can also be due to allergy