it shouldnt be possible when connecting to a larger tv it just scales 1920x1080 to the bigger almost like zooming in, unless the tv ws 4k and your card couldnt handle when the default res was set
if your TV's HDMI output was badly enough damaged anything is possible. I would avoid using that HDMI connection ever again, until you can get it looked at by a TV tech. Wouldn't be the first time an external component of my PC fried a part/whole rig. electricity is a real buzz kill that way.
I would try to reseat your video card just to be certain. Attaching the hdmi (dvi/ DP, etc) can push the card out of the PCIe port sometimes and cause issues.