There are several possible causes of a sore throat
without other symptoms like runny nose, fever, and cough.
First, sometimes the throat can become irritated from things that you are ingesting. Spicy foods can sometimes do this, and smoking is another common cause of chronic sore throat. If you can identify anything like this and eliminate it, the soreness should get better.
Another common cause would be acid reflux or heartburn. When the acid in the stomach washes up into the esophagus and throat, it can cause a mild chemical burn which can lead to soreness.
Next, this could be strep throat. Strep throat is a bacterial infection of the throat that is common and is characterized in part by bad sore throat without accompanying cold symptoms. It is more likely if you also have enlarged tonsils and swollen glands in your neck. If you think you have strep throat, you would need to see your doctor
to determine if you need antibiotics.
Finally, this could be just the start of a common cold. Sometimes, the sore throat will proceed the other symptoms (such as cough and runny nose) by a few days.
I would talk to your primary care doctor
if the symptoms continue or if you have more questions.