Civic - Honda :: 2003 EX Choking And Almost Stalling Out When Shift From 1st To 2nd Gear

I have a 2003 Honda Civic EX that is choking and/or almost stalling out when I shift usually from 1st to 2nd gear, but also sometimes from 2nd to 3rd. It usually happens after I've driven it for about 20 minutes upon coming to a stop (intersection/stop sign). When I finally go, I push on the accelerator but it feels like no gas is being pumped through with a loss of power. I repeatedly push on the accelerator until it finally kicks over and power is restored. My check engine light is on and I've had the diagnostics read from local parts stores and mechanics and no one can narrow it down. My mechanic said that it sounds like the valves were sticking but can't narrow it down to one thing without ripping apart the engine and going in deep, which would be expensive, but also not as expensive as a dealership.