Can Ice Packs Freeze Water at 21 °C?
It really depends on the initial temperature of the ice packs and their composition. If they start at a temperature far below the freezing point of water, they could conceivably freeze the water as their container comes to thermal equilibrium. That said, they’re going to have to be quite cold.

To cool by $1°\mathrm{C}$, liquid water requires the removal of roughly double the amount of energy that ice would give up in moving up $1°\mathrm{C}$ (per gram.) If your bags of medicine started at $5°\mathrm{C}$, (stored in a refrigerator) then the ice will warm by about $3°\mathrm{C}$ as it brings the medicine down to its temperature because it has three times the mass and gives up half as much heat per degree gram.

Once the water has reached $0°\mathrm{C}$, it will begin freezing. For every gram of frozen water, about $160~\mathrm{g}$ of ice will warm by $1°\mathrm{C}$. The entire mass of ice will be enough to freeze ~$2.3~\mathrm{g}$ of water for each degree it is below freezing.

Assuming the ice packs came from a normal freezer, their starting temperature is about $−20°\mathrm{C}$. They would warm to about $−17°\mathrm{C}$ in bringing the water to its freezing point. From there the ice could then freeze about $40~\mathrm{g}$ of the medicine before it all came to equilibrium.

Note: There are significant assumptions (notably, that the heat capacity of the ice pack is equal to that of ice and that its melting point is equal to $0°\mathrm{C}$) and some healthy rounding here. If the ice packs melted at a temperature significantly lower than $0°\mathrm{C}$, their heat of fusion could be sufficient to freeze the water, given time.