The sign for "sore throat" has a couple of widely used variations.
A very simple way to convey the concept of a "sore throat" is to do the sign "pain" near your throat.
Some people use this version to mean "pain in the neck."
SORE-THROAT / "neck hurts"
Also see: PAIN
Another common method if signing "sore throat" is to use a loose "G" hand. Move the "G" hand down your throat twice while looking pained.
SORE-THROAT (version)
Notes:You might see someone use a sign for "sore" that looks a lot like they are doing a mutated version of the sign for YEAR where the "S" hands are rotated around each other twice (while kept in close contact). That is a legitimate sign for "sore" and you could sign it that way and then point at your throat -- but I think the ways above are easier and more efficient and thus are "better" choices to use for "sore throat."
SORE (variation)
Notes: