Thanks for the query to H.C.M. Forum.
You got infection ( bacterial most probably) in the throat, that's why there are spots over tonsil
Pain in the neck and mild degree cough
are due to this infection.
Usually this infection is just from two days so antiseptic gargles will sufficient.
if still you will not feel better ,than consult an E N T specialist.
Hope I have answered your question.
If further any question I will help.