I have an electrical problem. I installed a ceiling fan with…

Your existing switch box does not have a neutral. It is only a switch leg. With the wiring in place you can not have both the fan and switched receptacle but you can change things and make the fan work.

Go into the box with the switched receptacle and see where the switch wires are connected. Look on the brass screw side and tell me if the tab is broken off between the 2 screws.

The tab would be on the receptacle as stated above, not on the switch. To make your new installation work you need to remove both wires from the switch and connect the white wire to the white from the new 14/3. Connect the black from the 14/2 in this same box to the switch or switches that will be used. Connect the black and red from the 14/3 to the switches that will control the fan and light respetively. In the receptacle box you must remove the black and white that feed the switch box from the wiring. Then connect the black wire to the black to the receptacle. Connect the white wire to the white wire to the receptacle. I advise not using the stabs in the back of the devices, but using the screws on the sides of the devices. Replace the receptacle if the tab was broken off between the 2 terminals on the brass screw side. You are allowed one wire on one terminal so pigtailing may be necessary if you have more wires in the box. You would pigtail all the blacks together and all the whites together and then connect the device to the tails. Always connect all the ground wires in each box and ground all switches or receptacles.