I have a shower with separate hot and cold knobs. The cold comes out fine but the hot water is trickling out. Is there a filter or cartridge behind the stem valve that is removable?

Shut the water off to the valve and remove the handle, bonnet packing nut and stem and washer assemble. Now turn the hot water back on to flush out the supply. You should have a strong stream, If not click back and tell me about it. Reassemble and test. Good luck, Tom

Do I need a special tool to remove the bonnet packing nut?

Nothing special needed here, a Crescent wrench or adjustable wrench should do it. Could be an old style valve stem and washer or it may be a cartrdige. A picture might help but as you start to remove things it should become apparent. Just post back with what you find because our directions are different for a stem than a cartridge.