A lump under the jaw lasting three months despite antibiotics is more likely a persistent swollen lymph node or a small salivary gland stone than an ongoing infection. The photo doesn't show any redness or skin change over it, which is reassuring, but a picture alone can't tell us what the lump feels like or confirm exactly what it is.
Next Steps
An ultrasound of the neck can tell these apart and rule out anything else, so ask your physician for one along with a basic blood count. If it turns out to be a gland stone, drinking more water and gently massaging the area sometimes helps it pass on its own.
Health Tips
See a doctor sooner if the lump grows, becomes hard or painful, or you develop fever, night sweats or unexplained weight loss.