I have had a swollen lymph node in my neck behind my jawline for 3 weeks. I have taken antibiotics and it hasn't gone away. What could it be?

Differnt. May be an infection not sensitive to the antibiotics you are on. Follow uo with your doc you may need a biopsy or change of antibiotic.
Hodgkins lymphoma. Quit worrying and go see your doctor to know for sure. Hodgkins is very treatable.
Watch them. Neck nodes can enlarge anytime you have throat infection(either head cold or strept throat). The nodes will settle down in 4--6 weeks.If the lymph nodes enlarge and become bigger then you need to be concerned and need to see your doctor once again to find out the cause.