Aceleration with hesitation

THE ISSUE
I have a Honda Civic 2003 with 1.7 liter vtec ENGINE AND 4 Cylinders with 162,000 miles on it, my check engine light came on and ever since I have problems with accelerating. I will put my foot on the gas and my car will kind of***** like its trying to get gas but cant. This only happens if the car has been off for 10+ hrs. Also had tune up about 1 month ago so I know that shouldnt be the problem. After driving my car for 50+ miles, it stalls & won't accelerate past 20 MPH. It will kick in after a few seconds of stalling, but then doesn't accelerate again (I press on the gas and it does nothing!), The engine is still running.. I'll press the gas, and the car doesn't accelerate. The RPMs drop down like I'm just coasting. Downshifting and flooring it doesn't help, then after about 5-7 seconds it'll start to go again. If I let off the gas and press again, the same thing happens. I'll be at a stop sign, then turn and I'll be going 20 with the pedal all the way down for a little bit, then the whole car will***** as the engine shifts and it finally speeds up. My car is running really weird at start up and wont accelerate. When I get to 20 mph my car won't accelerate, it is slow and draging. Why does it hesitate when I accelerate? It almost sounds like its about to shut off but doesnt and it shakes a bit. The****** HAPPEN while I am driving and trying to increase my speed by giving more. Once my car gets going speed is not an issue. It seems that I have to push on the pedal just a bit more to get it to go. And after a few seconds of dumping gas in my engine it seems to respond USUALLY with a body-throwback*****.

SECOND PROBLEM
My engine keeps overheating while I'm driving slow, stopping on stop lights, in traffic, or I am parked in a parking lot with my engine on and listening to radio and/or having my A/c on and in a few minutes I find out that the odometer is always the way up to HOT, HOT HOT. When I start driving again, it starts falling. When I accelerate really fast, for example, to pass a vehicle, the temperature shoots up almost immediately. When I'm on the highway, everything is fine.
FACTS
My transmission was reBUILT a few WEEKS ago, my car had been sitting for a few WEEKS (UPTO 3 WEEKS) before then.