Stalling at Idle

I am losing my MIND and any help given would be much appreciated.

I have a 2005 Aveo with 139,000 and it has a stalling issue. It happens when I've been idling for a few minutes. The car will kind of shake and shudder and the RPMs will go up and down. After a few seconds of that it will just shut down. It also happens sometimes when I start the car and start to drive. I'll press down on the gas and the car will shake and not really accelerate. Very rarely I'll be able to keep it from stalling at that point. Once the car is up to speed it drives fine though. It's only when I idle for a while (drive thru's and such) that the stalling might happen. It doesn't seem to have the issue when the engine is cool. EI when I start it in the morning for work I have no issue. (But I'm not sure if that matters)

The car has new spark plugs and I ran cleaner through the fuel system. There is no engine code. I took it to get diagnosed and they told me it was the EGR valve. I got a new one but the problem persists.

It is fine for going between work and home but it's a pain in my butt if I have to stop somewhere because if I turn it off and back on again, after a few seconds the shaking starts.

Please help! This is my first car post of any sort so if I left out any important information that you guys need, I'll answer it as best I can.

Did they give a reason for the EGR valve replacement? A frequent culprit is a dirty throttle body, which can also affect the Idle Air Control (IAC) valve which is attached to the TB. If cleaning the TB doesn't fix the problem, and the IAC is going bad, it can be replaced on the '05. Cleaning the TB and/or replacing the IAC are fairly easy and inexpensive DIYs.

Egr valve would be part of the warm up system, i would say/guess replace the temp sensor, in this time of year, your car always starts in fast idle, but with the temp outside, it need to stay in high idle after fast idle shuts down, not enough gas = stall. But that only lasts as a problem until the car goes into closed loop and the fuel is adjusted by the o2.

If you have no codes, are you currently still running the cleaner? I personally feel the cleaner might be enough to kill the car. It should really only be run through a hot engine and be done with it in my opinion, not prolonged throughout the take and sitting in cold temperature.

They didn't give me a reason and it wasn't until after I had it replaced that I suspected they just threw it on there to make themselves money. I replaced the valve and got an engine code for it. Turns out the part I bought was faulty. I replaced it and the code didn't come back. But I thought it was suspicious that I didn't have a code for it before when they told me to replace it. Their quote for it was almost $400 for the part itself and almost $200 for labor. I got the valve myself for less than $100 and it took five minutes to put in. Lesson learned!
I'll look into cleaning the TB this afternoon and see if it helps. I had the IAC valve written down as a maybe but I wasn't sure because it said something about stalling while decelerating - mine is always during standstill.

I know it probably had nothing to do with it but I replaced the thermostat yesterday. I stalled on my way out of the gas station later that day though. I ran the cleaner through a while ago actually just before I took a two hour drive to Delaware.

Thank you guys so much for the suggestions. I'll post an update on if they work. I have my fingers crossed!