Hi It's Dr. C. Board certified physician.
I'm sorry that you're having to deal with this.
Yes this is very likely lice. This is a very common condition in children. It's easily spread to others in the type of situation you describe, bed-sharing. Here is an information sheet about it:
The medications needed to treat this are available over the counter at any large store, Walmart, Walgreens, CVS, etc.
You'd use the shampoo as directed on the bottle. That plus everything in the fact sheet recommendations:
Follow these instructions exactly.
I hope all goes well and everything is back to normal soon.