I believe that HDMI 1.4+ cables are able to support 1920x1080 at a 120hz refresh rate, but you're usually best off using Displayport for 1920x1080 at 144hz. I know that dual link dvi-i or dvi-d (NOT SINGLE LINK, SINGLE LINK DOES NOT WORK) does support 1920x1080 at 144hz.
If you really need to, you can use HDMI, and make sure that you have set your refresh rate either in your AMD CCC settings or your windows settings. The R7 370 does support pretty much all connections including hdmi, dvi and displayport, so you've got some options.
If you want to see how to set your refresh rate using CCC, look at this screenshot:
Setting it using windows (7) settings:
If you still need any more answers, don't hesitate to reply.