For latency free monitoring you may want an external hardware reverb that routes only to your headphones. I do this via a Yamaha mixer with on board Reverb and other FX. My sound card/interface routes directly to the USB input while audio output and playback from the computer goes to the mixer. The mixer is basically a monitoring and routing device. I don't record the output of the mixer. Although I have the ability to go into the mixer first, route my vocal through the reverb, then to the headphones while at the same time having a separate "dry" output going into my Audio Interface I don't choose to do it this way.
There are Audio Interfaces that have Direct Monitoring and FX built in that allow you do do this.
For a make-shift you can blend in an outboard reverb unit like a guitar pedal between the headphone output and your headphones. Would be best if it were stereo. I have 2 hardware FX units that are stereo. With this you will hear the same reverb on your playback track as you hear on your vocals. Of course you need more cables for hardware stuff.

Does the noise in your head bother me ?