Radeon 7450 card
Catalyst version 15.7.1
Dell Inspiron 3647
8gb RAM, i5-4460s, 2.9Ghz
Windows 10 Home, 64-bit, 10.0.16299
HP 32 inch monitor, 2560x1440 capable
DVI-D cable, dual link version
No selection for anything higher than 1920x1080, now what?
According to the specs for your HP monitor it says it has 2 HDMI and one DP port for connection. How are you connecting the DVI to the monitor?
I have a ACER monitor that shows the same resolution as your Monitor. It is connected via HDMI. Unfortunately, the highest Resolution using HDMI on my Monitor is 1920 x 1080.
Try using Displayport and see if it shows the highest Resolution for your HP Monitor.
from HP.com specs on your Monitor: