Hard painless lump behind ear and on throat, been there 3 months or more. antibiotics didn't make them go away doctor not worried why they still there?

Lymph nodes: Likely they are lymph nodes--they swell when combating an infection in proximity, and can remain swollen afterwards for a few weeks to months...Or can become inflamed with repeated checking, so must walk a balance between not poking it and seeing if still there. If persists 4-6 months, may be reasonable to biopsy to see why still "up.".