a/c works but the fan is turning slow and has a clicking noise

I can't say for sure, but it sounds like there is some concern with the strength and speed of the blower motor. If you have manual temperature control (where you cannot set a specific temperature), then you have a blower motor resistor that acts to vary fan speeds depending on the selection of the fan switch. The resistor may not be functioning properly preventing certain blower speeds from working. If you have automatic temperature control instead, there is a blower speed controller that serves a similar purpose, controlling the variable fan speed depending on demand. Either way, you could also have a blower motor problem, or it could be debris, as experienced with your cabin air filter when you removed it. These are just ideas; troubleshooting is really necessary to find out what's going on.