Is it normal not to be able to lift your head off the floor when lying down flat after having Botox in the neck bands?

The muscle that lifts the head, called the platysma, is the same muscle that causes neck bands. Injecting the bands will weaken the platysma. In some patients, there is a fine line between achieving a nice cosmetic result by eliminating the bands and not weakening the neck muscle so that it is hard to lift the head.
The platysma's weakness will resolve as the Botox wears off. Ask your doctor to inject fewer units of Botox in this area next time. 

Thank you for your question. What you are experiencing is not unusual and as long as you are not having difficulty swallowing there is no significant problem. However, this should get better over the next couple of weeks. Please make you injector aware of this. Best of Luck!

While some weakening of neck muscles maybe possible after Botox injection for neck bands, it's not something commonly seen with conservative does. I usually inject 8-12 units per neck band and don't inject more than 50 units into the neck. This avoids most issues. That being said, as long as you are not having any difficulty swallowing, there is nothing to worry about. The Botox will wear off over the next 3-4 months. 

Thank you for your question cochondinde. I am sorry to hear about your
situation. Botox is a purified protein used to address wrinkles associated with
facial expression. Botox can be placed in the platysma muscle in the neck to address neck bands. If it spreads to the nearby sternocleidomastoid muscle (which flexes the neck) this would be weakened and one would have difficulty. Please follow up with your doctor for specific recommendations. Good luck!

It is not unusual and as long as there is no difficulty swallowing there is not a significant problem, this should get better over the next couple of weeks

Hello, and thank you for your post. I certainly counsel of my patients to expect a bit of weakness with certain neck excercises when treating neck bands. The muscles of your neck support a great number of skeletal structures and this is to be expected. For my patients that are very yoga active, I counseled them that it may be slightly more difficult to hold certain poses, but it should not be as limiting as perhaps you are describing. Seek the expertise of a board certified provider.
Dr. M-D.

it is absolutely not normal to have the symptoms you're describing.  I would get in touch with the physician who treated you or go to an emergency room.
 Good luck from New York City