OOOf! Sorry to hear of your illness and your friend's handbag. Double woof!
I would guess that your 1st day of induction and your illness have little in common as your body would not have had time to purge itself of the carbs from the previous day.
There is a virus (or whatever) that is going around that had me and others sick for several days recently. Wonder if that could have anything to do with your movie experience? (I hope not!)
Speaking for me (and your mileage may vary), I plowed thru the withdrawals by the middle of the 2nd week and then began feeling much better til I came down with the creeping crud (virus). Great news is that by staying the course and staying on induction by the time my illness had passed I was feeling better than I have in years. Literally.
Again, each person is different so I do not propose that my experiences will match yours. I would suggest that you try to follow your chosen way of LC eating until you see if your illness and the eating program have a direct link.
It could be that you are super sensitive to changes in body chemistry...but it is also very possible that your illness had no bearing on your eating plan.
Good luck and best regards!