The medications you are taking do not have any serious interactions with each other. It will be hard to determine exactly what caused the symptoms you described, but it was likely the hydrocodone. It can cause severe nausea, stomach pains, and dizziness. People occasionally have a bad reaction to hydrocodone even if they have taken it before. The symptoms you experienced were probably not due to an allergic reaction because they resolved so fast.
it sounds like you had an allergic reaction or OD to the Augmentin. My Mom nearly died from Augmentin. It is a very strong drug and sometimes doctors go over board on the dosage. Don't take anymore. Call your doctor and get a different, less harsh antibiotic.