Please don't worry. It is not at all serious.
The mass just below your jaw is most probably a lymph
gland. This enlarges and becomes visible if there is inflammation in it usually due to infection. This gland gets secondarily affected from primary source of infection in throat, nose, sinuses
Your doctor would have seen the inflammation in your tonsils. So he said so.
Rarely the source of infection may not be found. But the treatment is with antibiotic.
It would have been better if you had written what antibiotic was given.
Mostly the micro- organism is not sensitive to the antibiotic given by your doctor. That is why the mass is persisting.
Usually this responds to Co- amoxyclave (antibiotic) taken for 5-7 days with anti-inflammatory.
You please consult an ENT specialist