I accidentally took the wrong birth control pill- I took the one you would take the day before you get your period instead of the one I was supposed to- I should have taken the one at the end of week one. I was very sick the next day, vomited several times, and have been experiencing nausea and headaches the last four days since. Could I be experiencing side effects from taking the wrong pill?

This doesn't sound typical of a mixed pill. I would get this checked out.

The big danger with taking the wrong pill is that you may not have the full protection you are expecting. You should not be puking.

I see no reason for being sick, ( you should have it checked for being sick)

Now as noted your birth control may be less effective so you should be using other methods for at least a month