04 sonata engine stalling on reverse and other...

[tnad]

Hi,

5 months ago, I started having a problem with my engine shaking and sometimes stalling on reverse with my hyundai sonata 04 (low mileage: 13k). The engine also shakes occasionally when the car moves forward, especially when it's stopped and my leg is on the brake or when I'm starting to move forward from brake, but never stalls on forward. I also noticed that many times when I accelerate to higher speed I can feel this weird and often strong shake in the engine like it's struggling to go forward but needs a lot more gas than usual. This problem is usually solved when I give it enough gas and get to 50 mph or higher. I took my car to the dealership and they said it was a problem with carbon buildup in the engine because I don't drive my car that much and they did a 2-step (or 3-step) cleaning. This cost me $200 even though I'm still under full warranty. They said there is no problem with the car and this is not covered by the warranty. Anyways, this cleaning solved the problem for about 3 weeks even though I could feel some small shaking from the beginning. The problem is it just got worse and worse over the next few weeks and now I'm back where I started with the stalling and shaking. I'm afraid to go back to the dealership and pay a lot for cleaning again. Do you think it's carbon build-up? Is there a way I can fix this myself. I'm not that good with fixing cars but can definitely learn quickly if someone points me in the right direction. Thanks.