Thanks for your query.
With the information available he seems to have got throat infection
It is unlikely to be due to HPV shot allergy
though as a minor adverse effects the vaccine
might cause some cold like symptoms such as runny nose, a sore throat
or a cough.
Kindly get him checked for throat infection that might need specific anbiotic.
In the mean time give him panadol & sips of warm fluids . If he has breathing difficulty consider visiting ER.
Hope you find the info useful.