Botox is extremely safe, but while the risk of side effects is very small, it is not zero. Various things related to the Botox treatment could cause a rash, none of them the Botox protein itself. For example, sometimes Botox powder is mixed with preserved saline, and people can be allergic to the preservative. Some doctors (not many) use a topical anesthetic cream: again, another potential source of allergy.
However, having a rash 6 weeks after the treatment that isn't getting more and more severe, leads me to question whether it was the Botox treatment itself that started the rash, or something else you may have started using at the same time (Retin-A type cream?).
To best unravel this mystery, see either the physician who did your original treatment, and/or a board-certified dermatologist to start investigating.