When Botox is injected in low concentrations in between the layers of the skin. It acts as a chemo-denervating agent, which blocks nerve signals to susceptible skin structures, such as sweat glands, apocrine glands and small skin blood vessels to prevent their normal activities. As a result of this chemo-denervation, there will be less sweat, less body odour and less flushing.
The other topical treatments that you have mentioned acts either directly on the skin blood vessels to constrict them (e.g. bromonidine) or indirectly by reducing skin inflammation contributing to the erythema (e.g. metronidazole).
However, do be careful when using botox. Do not add excess botox as it can cause Botulism, an illness which can cause respiratory failure and is also proved deadly.