There is no problem with using black seed cream for a breastfeeding woman, and black seed may even be taken internally, as it can increase lactation. However, she should make sure that the composition of the cream is not harmful to the baby.
As for using black seed cream for her child, this will be possible but in a small quantity, and the cream should preferably have been made in a laboratory.
What the science says: black seed (habba sawda)
What the published research says about the remedies mentioned above, as context — these studies address material causes, but healing belongs to Allah.
Black seed (habba sawda)
A prophetic remedy par excellence, black seed is today one of the most studied plants: recent reviews detail its anti-inflammatory, antioxidant, and immunomodulatory properties, driven notably by thymoquinone (Int J Mol Sci, 2024) (Asian Pac J Trop Biomed, 2013). Its effects on vascular inflammation were the subject of a dedicated review (Front Pharmacol, 2021) and its action on immunity is documented (Int Immunopharmacol, 2015). Precaution: black seed oil is potent; at high doses it can lower blood sugar and blood pressure — use caution if you are being treated for diabetes or hypertension, and seek advice during pregnancy.