Am I being a bad parent?

You're sick, you're a mom, and you're doing the best you can. You're not slipping her Hot Toddies (which my roommate's mother used to do!) and there's sugar in other things that babies eat. A little bit for a few days won't hurt the child. The fact that you're concerned with it points up the fact that you're a good mommy. Stop worrying, and try to get some rest.