A swing ride jerks the neck exactly like a mini whiplash - the strap muscles get sprained and even swallowing tugs on them, which is why it hurts when you drink water. That part is muscular and settles. What I want to be sure of is that there is no throat infection or lymph node in there, since neck pain plus painful swallowing can also be tonsillitis.
Next Steps
Warm compress twice a day, gentle neck movements (no cracking, no collar), plain paracetamol for the pain and warm salt-water gargles. Should ease in 4-5 days. Do not wait if you get fever, difficulty swallowing solids, a lump in the neck, or tingling into the arm. Message me on a Practo consult and I will prescribe a proper muscle relaxant course if it is still hurting.