Is it a mechanical mouse or an optical mouse? A mechanical mouse works by the ball turning a couple of rollers inside the mouse. The rollers are pressed against the ball and turn when the ball turns. If there’s dirt in there it can cause the rollers to slip against the ball, and they won’t register the full movement of the mouse.
A mechanical mouse can act like a miniature vacuum sweeper. The internal mechanism needs to be kept very clean (use a Q-Tip+alcohol and dry it after cleaning).
You might like to get an optical, wireless mouse. Monoprice has them for $10 plus shipping. There are only two drawbacks to these: (1) You need to change the battery(ies) occasionally, and (2) they won’t work on a glass-topped table without a mouse pad. Minor drawbacks, methinks.
Late edit: You do know that there is a way to control the mouse movement speed in the OS, right? In Windows, it’s in the Control Panel. Could that be your problem?
Ok, now I’m confused. What do you mean by the “wheel”? Do you mean the scroll wheel on top of the mouse? An optical mice does not have a ball underneath so I presume you didn’t mean to refer to a ball as the “wheel”. And I’m a little unclear about what you mean by “open it up and take out the dirt” which isn’t usually necessary for an optical mouse. What is the model number of your mouse?