Hair botox or keratin smoothing treatments like this use strong protein formulas, and some versions still contain formaldehyde releasing ingredients. Nothing applied to your hair and scalp passes into breast milk in any meaningful way, so this isn't about your baby ingesting anything. The real concern is the fumes you breathe in during a long salon sitting.
Next Steps
Ask the salon for this product's full ingredient list and skip it if formaldehyde or formalin is listed. Pick a well ventilated salon, ideally with a window open or outdoor seating, and keep the sitting as short as you reasonably can.
Health Tips
Stop and step outside for fresh air if you feel breathless, dizzy or get a headache during the treatment. Mention this to your dermatologist before booking it, since breastfeeding should factor into the choice.