What's the best way to get rid of a sore throat and runny nose?

Cold: It depends on what causes it. If it is a simple cold - try neti pot nasal rinses, salt water gargles. I like Ibuprofen as it helps the pain and inflammation. And, most importantly, fluid support! if there is another cause to those, you will need to elaborate on that.

Depends: Sounds like a viral infection and thus only time would get rid of it. Most colds from a virus go away after 7 to 10 days if not sooner. If the sore throat is bothersome, otc sore throat products may help. For the runny nose, if too bothersome, ask your doctor to prescribe a nasal spray for you to try.