Its normal for the 4890 fan to increase speed when the GPU works such as when playing games. You can use CPU-Z and CPU-ID to get temp and voltage measurements(CPU, GPU, Memory, etc) while your PC is running. CCC also display the actual GPU temp and fans speed when your PC is running.
Does it sound like the fan is actually hitting something or is it just an annoying whirring? Sometimes fans can be annoying, but it's only a problem if it sounds like it's making contact with something. Which card do you have specifically?