Cooling system and A/C

Chevrolet Malibu, v-6, 3.1L. Two days ago my wife drove the car and said the A/C was blowing hot and the temperature gauge was just over the half way mark. I drove it today and the same thing except the gauge went to about three quarters driving in traffic below speed limit, still no cold air. The A/C clutch was not engaged and I cannot hear anything so I do not know if the radiator fan is even running. It did not even cross my mind to look at the fan. Duh. I moved to Arizona from Ohio a year ago and we have had triple digits for the last two days. Do I have an A/C problem, a cooling system problem or both? Coolant bottle is full. A/C was charged about this time last year but a new charging hose gauged in the red at 100 psi on the Freon last night so none was added. No leaks of coolant present nor white build up on water pump. These systems are independent but rely on each other correct? Where and what should I check first? Any suggestions appreciated.