You'd probably get fizzy drinks if you put dry ice in them! We used to have a gadget that dispensed fizzy water that used a bottle of water and a little metal capsule that probably had hi pressure CO2 in it.

I imagine the manufacturers just bottle the soda while it is under pressure.Some CO2 goes into solution until you open the bottle and release the pressure. Why do you think they use carbon dioxide? Does temperature effect how "bubbly" soda is?