Weird problem with my civic manual.
 

I was driving to work and noticed that when I switched gears, meaning when I let go off the gas and pressed in the clutch the rpms would continue to increase for a little while and then fall. Usually when I released the gas and pressed in the clutch they would fall.

Also when I parked at work and put it into neutral there was a loud grinding sound while the car idled.

The grinding noise stopped when I turned off the car but from now on the weird rpms shooting up when I press the clutch continues to happen.

Any ideas? I want to get several advices before I go to take my car in to get repaired.

Generally if the revs jump after you press the clutch in it's because you held the gas too long.

From where did the grinding come?

describe the grinding better.

OK. After I parked and put it in neutral it made a grinding noise until I shut the engine off. For about 20-30sec.

The noise didn't go away until I shut off the car. After I restarted the car 2 hours later there was no grinding noise.

For the reving problem I released the gas pedal, waited 2-3 seconds then pressed the clutch in and the rpms still increased. It won't go away.

The grinding noise came from the transmission. 20-30 sec was enough time for me to hear where it was coming from. All the gears still work but the revs increase everytime I press the clutch in has me worried.

This is the time when you need a tach, to be honest, not trying to give you a hard time, but it would be really good to know from where to where it went and all that. :(

It goes plenty up for me to hear it from the cabin

Two major contributors to unloaded engine RPM: idle air control motor and throttle. If your engine is cold it wants to idle high. If you shift at super low RPM then it's possible that the engine is trying to get back to it's high idle for warmup. (This happens to me when I shift to N from a slow 5th gear cruise in the morning).

A 99 Civic shouldn't have any of that throttle by wire nonsense, so you can check the linkage for lag.

Check engine light?

As for the griding, are you sure it was a grinding? Like a bad shift? Or was it more of a rattle? You get rattles when exhaust flashing comes loose, and might sound like a grind I guess. I just don't buy that it's definitely in the trans unless you stuck your head under the hood with a mechanic's stethoscope. It's nearly impossible to pinpoint internal noises any other way.

Your throttle cable could be gummy also, resulting in a slower return to 0% throttle. I would be more likely to suspect a mal-adjusted FITV or some other idle control component.

Dax you are right. My whole engine compartment is clean but my throttle cable is super dirty where it attaches to the TB.

There is no check engine light. But you are right also. This did happen in the morning and I do shift at super low RPM. I will check the idle components.
The problem even stayed after the car warmed up so now I'm confused about the car being cold.