What Could Be The Reason For Throat Pain And Neck Pain Only From Right Side ?

I’m 35 years male, 3 yrs smoking history (3 pack/year history). I had mild pain in my neck next to my throat right side from 4 weeks ago, actually the pain seems like muscle or nerve pain , It appears when I blowing an balloon for example, and when blowing my nose, recently from 1 week ago I had mild pain when I press on my throat (right side) so I went to Otolaryngology (Ear, nose throat), he diagnosis sort of throat infection form using Air Conditioner as he said. So he put me on antibiotic Klacid (Clarithromycin) for 1 week, now after I’ve done from Klacid, I don’t feel the pain when I press on my right side throat, but I can feel the mild pain on my neck right side only when I blowing, and sometime when yawning. What could that pain? Many thanks.