Part of display not working, changing display region for macbook pro
I was wondering if I can do something so that my entire screen appears in only the part to the right of this black portion,

No, this cannot be done.
Your screen is physically damaged, but as far as your GPU is concerned, it's working fine.  The dimensions that get reported back (for example 2650x1400) are still reported back.  It has no idea it's now only (making up a resolution here) 2300x1400.  And even if you were able to tell the driver that was your resolution, it would be centered, not shifted left/right.
Your best bet is, if you must use the machine until you can take it in, to get an external monitor.  They're inexpensive and fairly reliable. Also, an iPad, iPhone, Windows, Unix or Mac computer can screen share very well using several apps.
There’s no harm in running a Mac with this display damage and using another display - especially if it’s stationary or running closed clamshell.