First, there is no such thing as "1600p" for resolution purposes. Not sure if you're referring to the older UXGA standard (1600x1200, 4:3 aspect ratio) or its widescreen cousin UWXGA (1600x768, 16:9 aspect ratio), but neither one of those is truly HD. I suppose you could have maybe meant the WQXGA standard (2560x1600, 16:10 aspect ratio)...but again, although used for home projector systems, it's not a true HD standard.
"1440p" exists (aka QHD/Quad HD, 2560x1440, 16:9 aspect ratio), with 4 times the pixel density of 720p (1280x720, 16:9 aspect ratio), & there are 27" or larger monitors/TVs that can display that resolution. However, for HD formats the number portion shows the number of vertical pixels...& there are no HD formats with 1600 vertical pixels; the closest is WQXGA+/QHD+ (3200x1800, 16:9 aspect ratio), but that's so far been limited to laptops.
The problem for you, though, is that with a 22-24" monitor you won't really see a whole lot of difference between 720p & the higher standards. You need a bigger screen to really see any differences. Which is why I find it really ridiculous when they talk about a 7-10" tablet or a 4-6" smartphone screen having a higher resolution than my 32" TV set: you can't really see the difference that you're paying the extra premium for.