Yes, you are wrong.
A doctor might say "In 9 days, you can remove the bandage." Or he might say "After 9 days, you can remove the bandage."
Either way he does not mean to do it tomorrow. It means wait until 9 days are over.
What you were describing is "in (or within) the next 9 days." Say you need to go get your driver's license renewed before it expires. You might tell someone you need to do this in the next 9 days.