How long does it take for amoxiciolen to take down the swelling in my face?

Hard to say: Depends on how large the swelling is, and how the infection responds to that antibiotic.. You may need a different one. Did your physician or dentist prescribe the drug? If so, discuss it with them. If you are self medicating, then call one of your providers for an appointment.

Too broad a question: Is the swelling due to an infection? What's causing the infection (tooth, gum, other structure)? Acute or chronic? Where is the swelling? What is the dosage and frequency of the amoxicillin? What is your age, general health and any medical conditions? The list goes on..... Have the dentist or physician who is treating you answer that question. I assume\hope you are not self medicating yourself!