Hi and thanks for the details.
These glands that are swollen are called sub mandibular lymph nodes. These receive lymph afferents from the right side of the lower teeth, submandibular salivary gland and right lower half of the face and the right lower side of the jaw.
Any infections or chronic inflammatory process going on in these regions will make the glands swell up.
Viral attacks like the head cold that you experienced can also make them swell up. Chronic inflammation does not make the glands painful to touch however, and that is a sign of something recent going on.
I suspect that you may have a dental sinus infection or gum inflammation of the teeth on that side of the mouth.
However, sometimes, lymph node enlargement like this one does not have an underlying cause and is self limiting and subsides in a few days.
You might need to get your PCP to have another comprehensive look on them and a few tests like Fine Needle Aspiration Cytology and Full Blood Screen with an ESR may be helpful in defining an etiology.
Antibiotics are not helpful unless, you know the cause of inflammation and the pathogen involved and are only warranted when there is fever. So your PCP was right in not starting you on one immediately.
Use the anti inflammatories for a week and if the glands do not decrease in size then further workup is advised.
OCPs do not cause lymphadenopathy. If you think your contraceptive pill is not good for you then I suggest you substitute it with another one.
--Hope this helps--