The side effects on AD's can go away after 2-4 weeks. Some people dont do very well on Zoloft and they get the side effecst all the time they are on it, but they can go away. I have never been on Zoloft but I know people who have and have been alright after a couple of weeks.
I hope this helps
Vicodin can cause nausea and vomiting and together with Zoloft which can cause nausea you may have your answer. You said you take other RX meds so it may be the whole combo.
You may want to check back with your MD if the vomiting continues as you could become dehydrated. I wish you the best.