I've never had a real problem with an impacted wisdom tooth. But I have had a tooth infection and a horrible toothache before, where I had to be on antibiotics and pain medication. The dentist prescribed the same thing for me, 500mg of Amoxicillin, and also 800mg of Ibuprofen for pain. One time, the pain was so severe they gave me Vicodin. I don't know what an impacted wisdom tooth is like, but I can tell you that an abscessed tooth is excruciating.
Amoxicillin will kill the infection and the pain will start to ease up, but it may take a while. The doctor or dentist who prescribed the antibiotics should also have given you a strong pain medication. The antibiotics will treat the cause of the pain (infection), but it will take time. Go back to the dentist and ask for pain medication. In the mean time, Ibuprofen will help with the pain and swelling. You can get 200mg Ibuprofen over the counter.
The Amoxicillin will definitely keep the infection from spreading, as long as you keep taking it as directed. I remember when I had to take it, it seemed like it took a while to start working for me too. I didn't notice any real improvement for at least 2 or 3 days. But it will work. If it seems to be getting worse, definitely go back to the dentist. I don't know if Penecillin is stronger, but for a really bad infection you might need a stronger antibiotic. Usually, Amoxicillin works though.
Another thing is try to take it easy...don't do any exercise or heavy lifting, because that will increase your heart rate and make the imflammation worse. That will cause even more pain and swelling. Right now, you just want to be calm and take it easy, and let the medication work. This is one time where you definitely have an excuse to just sit and watch tv or play on the computer! :)