In your condition the sneezing and runny nose could be due to either chlorine allergy, poor water quality or poor ventilation. Drink about 4 liters of water a day to ease clearing of secretions from the throat. When there is not sufficient water in your body, thick mucus forms which can be difficult to cough out and has that sensation of being stuck back of your throat.
Next Steps
Consider changing your swimming location, if the problem persists then get a pulmonologist consultation to look for airway hyper reactivity.