How Safe is Botox?

I think you’re referring to an animal study and not humans. Botox is very safe as it has been used for more than 30 years at high doses for neurology patients, much higher than that used for cosmetic purposes.
It is possible that if some Botox got in to a blood vessel that you might feel nauseated, or it is the technique of pain management during the delivery of the product that can cause this.

Botox has been in use for some 20 years, with millions of injections performed and its safety record is one of the best. Your question is a good one though. The report to which you are referring caused quite a bit of consternation so it is good to set the record straight. It was a study done on rats, not people, in which botulinum toxin injected into the face appeared in trace amounts in the brain several days later.
The type of botulinum toxin was a veterinary grade, and is what is called "uncomplexed" which means that it is a much smaller molecule than the type used in Botox. Smaller molecules are much more likely to migrate. Further, the dose used was about 150 times greater than what would be used in people, and despite all that no adverse effects were noted. I think your nausea reaction is unrelated, as that can happen after any type of injection.