Can you accidentally swallow a piece of dust or hair? i always get a feeling that there is dust in the back of my throat or tongue.

Yes: Everybody always swallows dust particles and other debris on a regular basis without any problems. This is not the cause of the feeling you have in the back of your throat. It is caused by a local irritation or even a post nasal drip.

Post nasal drip: You should consult a physician. You may be suffering from allergies and postnasal drip.. Allergy medication like antihistamine and nasal spray and neti poti sinus rinse can help. Consult a physician or an ENT specialist.