Probable Virus. More than likely you have a viral sore throat. It could have associated fever, a white covering on the tonsils and back of the throat, swollen lymph glands in the neck, under the jaw and you could even have a rash. Strep throat could do the same. If you have not ingested anything to cut or abrade the throat or back of throat, then viral would come to mind, though others could cause this.
Throat Being Cut. Swallowing should not hurt. Need to know more about "cut". I suspect you have had a recent viral throat infection. If symptom is more chronic, try prilosec, 1 / day for fourteen days. If not cleared afterwards, see your doctor. Sometimes, nerve inflammation, neuralgia, can cause the feeling of being cut. This may respond to medications for neuralgia.