Can I Get Botox for Sweating Below Breast and Groin?

What you have developed is compensatory sweating - that is, sweating in your lower body following endoscopic thoracic sympathectomy (ETS). Compensatory sweating is more likely following ETS for hyperhidrosis involving the head and neck than for ETS performed for hyperhidrosis of the underarms and/or palms.
Yes, Botox can be applied to areas where you have compensatory sweating but this is usually a very expensive treatment option as the surface area involved can be large - such as the back, groin, buttocks, behind the thighs and knees.
Beyond cost considerations, it is not pleasant to be injected with needles in large areas of the body. Topical anesthetics can be used to reduce needle stick-related pain, but areas such as the groin are very sensitive and need approximately 10 needle sticks to provide enough Botox to cover approximately 4% of the body surface area.
If your compensatory sweating is limited to the groin, then Botox can be injected and this may be an effective option for you.
Again, it is not practical to inject large body surface areas with Botox to treat compensatory sweating.