call your pharmacist, not all antibiotics have to be refrigerated all the time, but keeping them cold just helps they stay mixed together better/longer but as long as you can shake them up really good and refrigerated after you arrive (assuming you are non going to China or Australia or something like that). you can usually carry less that 4 oz of any liquid item onboard a airplane, one quart size zip lock baggy filled with 4 oz containers per person, so you may want to ask the pharmacist if he can put the meds in smaller containers labeled if needed. hope that helps... calling the airlines can help also, when I worked as a Flight Attendant we were taught that the airlines can not refuse you the right to carry on board any medically necessary medical supplies/medicine, although needles were managed with security procedures.
I've heard that Spirit Airlines is a bit difficult to work with and charges per carry on, you you might want to be sure you can easily store your cold back/medicine bag inside you regular carry on or purse, just a thought.