After getting Botox on my forehead, I developed a hive -like rash on my chest and back. Is this normal?

I have never seen an allergic reaction, hives or rashes develop in a different area than what was treated with Botox. I think this is likely a total coincidence. Even legitimate allergies and reactions to Botox are extremely rare. One possibility is that you may have had an allergy or sensitivity to whatever was used to dilute the Botox. However, this also usually happens at the site of injection and not in other areas. A small number of people get headaches after Botox. This is also unusual as we use Botox to treat headaches! But it does happen sometimes. 

Allergic reactions to botox is extremely rare. It is more likely that the rash is coincidental especially that the rash occurred on the chest and back rather then at the injection site itself.   

This would be very unlikely. I have never seen an allergic reaction
to Botox – especially at a site that was not injected. Mild redness at the injection site is
common, and even mild bruising may occur. However, a diffuse rash on your chest and back would be very unlikely. Most likely, this is a coincidence and
if the rash does not resolve, I recommend sharing this reaction with your injector would be
helpful for them to be able to document. I wish you luck and hope your rash resolves soon!