Dear OP.
Upgrading to a 144hz monitor, will most likely not yield any noticeable difference.
However, if upgrading to a 144hz display that has adaptive sync, you can enable G-Sync in the Nvidia control panel.
Having G-Sync will allow you to have your frame rate in games uncapped, and will allow them to fluctuate as they do, and you won't get any screen tearing.
Along with no screen tearing, (which without adaptive sync requires V-Sync) you get lower latency than you do when using V-Sync.
Furthermore, it will be useful in the event that you play a game that your current GPU can push higher frame rates in.
On top of that, in the event that you get the money together, and decide to upgrade your graphics card and get more frames, you will be able to benefit from that as well since you will already have the 144hz monitor.
But as it stands, with your current settings, and current performance in game (that you have stated, as that is all the reference I have at the moment) you will not necessarily experience a major difference compared to using your current 60hz monitor.
So upgrading will instead come down to what I just said, which is improved experience in the event that you play a game that your GPU can push higher frames on, and/or upgrade your GPU for higher performance (more frames)
Hope this helps answer your questions.