Only the right side of my throat is sore. It only feels uncomfortable when I swallow, and even then it doesn't exactly hurt.?

Irritation. You can have one tonsil infected or irritated by something you swallowed. When you scratch the back of your throat it tends to swell up a little and that can cause one side to feel uncomfortable. You can also develop little "stones" in a tonsil that cause irritation. Try some salt water gargles for a day or two.