Hello. I'm going to tell you what happened with my 2012's A/C in case it helps you or someone else out. My A/C was also blowing warm, but the A/C light was staying on constant as it's supposed to (no flashing). I attempted to recharge the system, but found that the compressor was not staying on even when I had it on max A/C with the doors open. I should note my exterior, or ambient, air temperature sensor also registers the correct outside air temp.
I took her to the shop, and they first replaced the duct air temperature sensor, explaining to me that the A/C compressor was shutting off as it was reading the incorrect temperature (in my case, reading a temperature of like 140 degrees). When the part arrived, they replaced it but it did not fix the problem. The system was holding a charge, no leaks, so they determined it was actually the HVAC control module. I have the HVAC control module on order from gmpartsdirect.com, and will install when it arrives.
Thought I would share since I haven't personally seen anyone with this particular problem in our platform. Good luck with your troubleshooting!