A system may include a mobile wireless device and a carry bag. The carry bag may include a pouch having an opening therein, at least one divider within the pouch defining a medical container compartment and a storage compartment, insulation lining the medical container compartment, a temperature sensor carried by the pouch and configured to monitor temperature within the medical container compartment, a wireless transceiver carried by the pouch, and a processor carried by the pouch and cooperating with the temperature sensor and the wireless transceiver to send temperature data to the mobile wireless device. The mobile wireless communications device may be configured to generate an alert when the temperature within the medical container compartment is outside of safe storage temperature range.