All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
A breast-feeding woman, who fears for herself or for her baby and herself, can break the fast but she has to make up the missed days later. The Prophet said: "Allah has relieved the travelers of fasting and half of the prayer, and the pregnant and breast-feeding women of the fast." [Ahmad and others] Allah Says (what means): {…So whoever among you is ill or on a journey [during them]-then an equal number of days [are to be made up] …} [Quran 2:184]
If such a woman fears only for the baby, then she has to pay an expiation (i.e. feeding a poor person) in addition to making up the missed days at a later date. This ruling is based on the narration of Ibn 'Abbaas who said concerning the verse (which means): {… And upon those who are able [to fast, but with hardship]-a ransom [as substitute] of feeding a poor person [each day]…} [Quran 2:184] "This is a concession for the elderly as they cannot fast. They are to break the fast and feed one poor person per day. Pregnant or breast-feeding women, if they fear for their children can do likewise." [Abu Daawood]
Imaam al-Khattaabi said: “Pregnant and breast-feeding women have to feed a poor person along with making up the missed days because they break the fast due to others, i.e. fear for their children.”
Therefore, if you fear for yourself then you may break your fast and should make it up later and you are not obliged to pay an expiation for it. The ruling is the same if you fear for yourself and for your child too as understood from your question. But if you only fear for your child and you break the fast due to that reason, then you should make up the missed days afterwards and pay the expiation.
Allah Knows best.