I have been experiencing horrible anxiety and panic attacks since I was injected 4 weeks ago, read online this is very common.

Hi there -
This is a tough one. 
Botulinum toxin has been used for many years for medical conditions such as strabismus and spasticity with an excellent safety profile. 
However there have been a very few number of reported issues as it has become more commonly used.
When injected in high medical doses for conditions such as muscle spasticity, botulinum toxin can extremely rarely enter the systemic circulation in doses high enough to cause muscle weakness. The cases seen were seen mostly when botulinum doses were over 600 units and injected into large vascular muscles (so higher number of blood vessels able to carry the toxin throughout the body) 
These doses were MUCH MUCH larger than any cosmetic injections.
Also the side effects from such large doses were muscle weakness - not anxiety.  
When we inject even small doses for cosmetic use, there is a chance that the tiny capillaries in the skin and facial muscles could carry minute doses into the systemic circulation. Looking at the medical studies though, it really appears the cosmetic doses would be too low to cause weakness of muscles and would be undetectable to the patient. 
That being said, I have seen forums where people have described unusual symptoms after cosmetic botulinum injections which don't make any logical sense knowing what we know from its current safety profile.
Who knows what time will tell.
I would advise you to report your symptoms  to Allergan, the makers of Botox, at 1 (800) 433-8871. 
If there really were a syndrome, then the only way it could be confirmed, would be if it were reported repeatedly and studied. 
All of this, of course, doesn't help you right now.
Whatever is causing your symptoms is causing you a great deal of distress. Even if Botox were the culprit there is no reversal agent. The rare cases showing musculature weakness in patients receiving over 600 units resolved within 3 months. 
I would agree with the other  physicians.
Please see a psychiatrist as they have a larger selection of anxiety medications to draw from - hopefully one will help you.
I wish you all the luck and take care.

Botox is not causing your anxiety. Botox is bound to the neuromuscular junction in the muscle it was injected causing it to relax. Your anxiety is caused because you believe it is causing you harm. You have anxiety and panic attacks that were triggered by Botox injections, but not caused by the Botox itself. Ask your family and friends if you were more anxious than the average person before the Botox was ever given. You should see a psychiatrist/psychologist to help with this as it is unlikely to fully resolve even after the Botox completely wears off in a few months.