A sore throat might mean you have a cold, and dairy products like milk will create more mucus. Like Wlrddiva and lunger suggest, try some throat lozenges, warm tea (with honey helps), or warm water with lemon and honey. If your sore throat persists for more than 2 days or you develop other symptoms, you should take cold medicine or see your doctor.
Warm milk can be very soothing to the sore throat but cannot alleviate the pain on a long term basis. You can take a sip of some warm mile but try some thing such as chloroseptic or suck on throat lozenges to help with the sore throat. If the pain continues for more than three days you should consider seeking medical attention.
I would suggest drinking warm tea instead of warm mile, like Wlrddiva said it can feel soothing at first but in the end may not make you feel better. After drinking your warm tea try sucking on a Cold-Eeze, these always help my throat feel much better!