The only way you will get the message about not moving your stick so fast is when the output of your stick is moving too fast. If your not touching the stick, it sounds like you have a harware problem.
You are correct when you started thinking that its the game. It is. You are playing an on-line game with hundreds of other players. If you stick output is that eratic, then we would see your plane flopping around like a fish out of water.
If you want to continue to use this stick, you may need to take some time adjusting each axis in the setup. Turn down the sensitivity on the sliders, and increase the dampening until you do not get the message. If you could sit and watch an experiance pilot play the game, you would notice they have very smooth stick movements, not jerky. If your smooth enough with the movements, and you have some good hardware, you can increase sensitivity of the stick.
Another problem looks like anger management. This game has a high learning curve. It takes time to get your stick set up so you have good stable flight. It take time to learn how to fly, then how to fight. It takes time to learn each aircraft you fly and the aircraft you fight. You will be up against some of the best sim pilots in the world. Your going to have to get some experince to do well here. If you can't control your anger, this may not be the game for you. If your up to the challenge, welcome to the unfriendly skies.
Gunner