The vicodin has a bad side effect of nausea which can result in vomiting. From my own personal experience, I had all my wisdom teeth removed last year and took a vicodin while I was still numb in anticipation of the pain and felt nauseous and threw up. So I would discontinue the vicodin for now. Vomiting from antibiotics could be a side effect as well but I'm thinking it may be more due to the vicodin also. So how many days of antibiotics have you taken so far?
Amoxicillin is similar to augmentin. Augmentin is basically amoxicillin with an extra ingredient in it. So you're basically taking the same antibiotic since you started with the amoxicillin. Your dentist can try another antibiotic such as clindamycin but its very strong and can cause stomach problems such as diarrhea, stomach pains, etc but clindamycin is great at killing oral bacteria.
Omnicef can be used too if you're concerned about the clindamycin's side effects. Omnicef, like all other antibiotics, can have similar side effects since it kills both good and bad bacteria though.