Not much study has been done on Pyrithione zinc during breastfeeding however it�s known to get absorbed in skin in some extant (Less than 1%). Topical usage is not likely to cause much problem but it�s suggested to search for safer alternative.
Dandruff | Pyrithione Zinc Lotion/shampoo is in the category of low risk, if you have already used it then its not a big deal if health and behavior of baby is good. However your health care provider shall be aware of the fact that you have used Dandruff | Pyrithione Zinc Lotion/shampoo so you should inform him based on your convenience.
Dandruff | Pyrithione Zinc Lotion/shampoo comes in category of low risk and if your doctor is aware that you are breastfeeding it should be ok to use
Not much monitoring required while using Dandruff | Pyrithione Zinc Lotion/shampoo
US
National Womens Health and Breastfeeding Helpline: 800-994-9662 (TDD 888-220-5446) 9 a.m. and 6 p.m. ET, Monday through Friday
UK
National Breastfeeding Helpline: 0300-100-0212 9.30am to 9.30pm, daily
Association of Breastfeeding Mothers: 0300-330-5453
La Leche League: 0345-120-2918
The Breastfeeding Network supporter line in Bengali and Sylheti: 0300-456-2421
National Childbirth Trust (NCT): 0300-330-0700
Australia
National Breastfeeding Helpline: 1800-686-268 24 hours a day, 7 days a week
Canada
Telehealth Ontario for breastfeeding: 1-866-797-0000 24 hours a day, 7 days a week