I'm going to not let my daughter in the hotel room because she has traveler's sickness.
That seems strange. Why are you preventing her from going into the hotel room?
I don't want her to get sick on the hotel's bed.
If your child is not feeling well, you should ensure their safety and comfort. Instead of keeping your daughter out of the room, you should purchase, or request, extra towels to clean up any mess that is made.
Ok, I will try to consider this in the future. But for this trip it is too late.
It is not too late, you can try to make her feel more comfortable now. It does not feel good to be sick and a parent should do more to make their kids feel good.