Overheating

I have an 05 Tahoe 5.3. I had a little issue with it overheating a few times over the period of the last six months. At any time I could be sitting at a red light idling or driving the temperature will go up to around 235 and then slightly come down I can put it in neutral and hit the gas a few times and it will regulate back to 210 but there has been a few times I could not get it to come back down and I’ve had to stop and put water in it or shut it off and let it cool down and then it has been fine. About a month ago I was driving home from work and not paying attention to the temperature my truck started to chime I look down my temp was at 2:60! I got to the nearest station shut it off let it cool down once it cools I crank it tried to add water but it would boil out of the reservoir and no radiator cap. We had to tow it home. We ended up changing the water pump the cool temp sensor flushed the radiator checked the relay for the fans nothing completely fix the problem. The issue I’m having now is it will heat up to 210 and stay there for a few minutes then it goes to around 227 we are bleeding the lines and when we do that it will cool back down to 210 for a few minutes but then goes back up to around 227. My heater no longer blows hot and my AC no longer blows cold my fans are no longer coming on either before they were. I know obviously I have an issue with the fan just don’t know why they’re no longer working and before they were. Also right before we decided to call it a night we were bleeding the line one last time and no water was coming out of the hose only steam but there was still water in the reservoir at this point we decided to shut it down. We’ve also checked the heater core rear AC and everywhere else for leaks at this point we’re lost. We also thought have a blown head gasket were cracked head because I didn’t get it so hot but no water in the oil no oil in the water no exhaust fumes in the water and no water coming out of my tail pipes.