I have swollen lymph nodes under my chin and neck what could it be I was recently prescribed amoxicillen and cipro (ciprofloxacin) will either clear my problem up?

Possibly, however .. You are describing enlargement of lymph nodes (lymphadenopathy) which are located in various places of the body and function as defenses fighting infections and other foreign material in the blood. You could have a skin infection in head/neck area, a tooth infection, etc. If the nodes don't go away after the rx, first see a dentist, and if that doesn't care of it, an ENT doc. Important.
Watch and wait. Agree with Dr. K. You may feel the nodes every couple of weeks, if any of the lymph glands doubles in size, becomes painful, ulcerates, or other nodes become enlarged, or you develop fever, or lose weight, you should see a doctor.