The celing outlet has one 3-conductor wire running to the wall outlet (black, white, red, ground). I hooked up the celing fan's white to outlet's white, the ground to ground and then ceiling fan's black to black. I also hooked the fan's light wiring (blue) to the outlet black.

FAN OUTLET
Gnd --> Gnd
White --> White
Black --> Black
Blue --> Black

At the wall there are two 3-conductor wires running into the outlet. I'm trying to install a new switch with a dimmer slider. The light works when the switch is turned on, it even dims. But when the fan is on and the dimmer is lowered, the fan motor slows down as well. I'm thinking that I should have hooked the blue ceiling fan wire to the red ceiling outlet wire. And then that red wire to the switch.

Right now the wire that comes from the ceiling has it's white wire connected to the second white wire. The red is not used. The gnd is hooked to the switch. The black is connected to the switch. The second wire's black is hooked to the switch and the red is not used.

Does anyone know if hooking the blue to the red and the connecting the red to the switch is the right way to go to solve my dimming motor issues?

If you have a spare red at the ceiling and the dimmer, then it should be used to dimmer only the lights, and leave the fan on the black, which will be un-dimmed, and the motor will now work properly.

If the 3 conductor runs straight to the control, you could also install a separate switch for the fan, connected to the black. So you would have

At ceiling:

Black-black
Red-blue
White-white
Ground-green

At control:

Black-fan switch
Red-light switch
White-neutral supply
And the other side of both switches to hot supply.

Ceiling fan wiring - Ceiling Fans N More