Hello, Dr Asif here. It is true none of doctor will agree to it. Botox is a neurotoxin and work only the muscle and sweet glands. There is no proven and scientific explanation of acne with Botox. On the contrary Acne is unpredictable, can occur anytime and anywhere. But your and other similar experience should be noted and researched.
I suggest you to go for Botox again. It wudn't matter Whatever you choose all botulinum toxin preparation contain Botulinum toxin A. So changing the brand wouldn't help that much.