To get the hang of it, it's a good idea to practice pumping for a few weeks before you need to rely on expressed breast milk for your baby. (babycenter.com)
However, thoroughly cool the freshly expressed breast milk in the refrigerator or a cooler with ice packs before adding it to previously chilled or frozen milk. (mayoclinic.org)
I would recommend if possible to keep up the pumping and bottle feeding of expressed breast milk at least for another month if possible, until cold and flu season are over. (justbreastfeeding.com)