Immediately after Botox, I have itching welt/hive. New doctor said no problem to try it again? (Photo)

There are many causes of wheals, raised swollen bumps that itch and may be red, including pressure, numbing creams applied prior to Botox injections, and possibly the liquid agent that is mixed with the Botox powder, and the albumin component mixed with Botox at the factory.  
There are preservatives in saline to which one may react.
You could consider having an allergist test you to Botox and if you do test positive, you may be able to tolerate Xeomin or possibly Dysport which are the same serotype of botulinum toxin as is Botox but they are produced slightly differently. You could have the same allergist test you to Dysport and Xeomin as well. This might be costly as I doubt any allergist has these botulinum toxins available and they would have to purchase them for just you, but that would be the safest way to proceed.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice.  The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs. 

We have not seen allergic symptoms like itching and swelling in any of our patients who received Botox without topical anesthetic. Occasionally, topical anesthetic (lidocaine, prilocaine, phenylepherine ointment) may cause contact dermatitis. If your treatment was not performed with topical anesthetic, consider calling Allergan to register an adverse reaction. Also consider consulting with a reputable allergist for an opinion before getting another Botox treatment. Hope this helps! Dr Joseph

I would do a skin test with a small dose of Botox in the doctor's office with some epinephrine ready. Although unlikely, it is possible to develop an allergy to anything even though you have had it many times before.