Codes P2277and P2099, number 2 Oxygen Sensor?

Yes, this can cause the engine to go into limp mode which sounds like what is happening. A bad O2 Sensor can cause this, but you may have a clogged catalytic converter as well or a bad turbo.

P2277: O2 Sensor Signal Biased/Stuck Rich Bank 1 Sensor 2. This code suggests that the oxygen sensor on Bank 2, Sensor 3, is sending a signal that is consistently biased towards a rich mixture.

P2099: Post Catalyst Fuel Trim System Too Rich Bank 1. This code indicates that the fuel trim (air-fuel mixture) is too rich after the catalytic converter on Bank 1 of the engine.

Let's go over these guides to help us figure out what's going on and I have included how to change out the oxygen sensor with the location in the images below.

https://www.2carpros.com/articles/how-to-replace-an-oxygen-sensor

and

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

Check out the images (below). Please upload pictures or videos in your response to the problem so we can see what's going on.

The codes you posted are valid GM codes but don't seem to be in the code listing for the car you have. That said there is no sensor #3, just the two next to the converter. One on top of the engine and one under the car just after the converter. I would try a different scan tool first, one that can read that vehicle and allow you to watch the voltages from both sensors to see what they are doing. There is a known issue with the GM vehicles in cold weather, they form ice inside the runners of the intercooler and can cause rich codes because of it. Basically, it chokes the airflow. GM issued a service bulletin on it. It basically says to insulate parts of the intercooler ducting to keep the air warmer during very cold weather. Perhaps an OE level tool can get you better results.