Studio apartment only has 2 prong outlets, I need to plug my PC into a 3 prong one
There is some cause for concern if you're getting a shock from the case of your computer.  There should normally be no voltage between the earth and the case.  Adding a green wire will bond the case to the earth and you won't feel that shock any more, but there may be current on that equipment ground wire, which is a problem.  So while grounding the receptacle is a good idea and a safety improvement, it may only mask a problem with your computer, not fix that problem.
Running a green wire (at least #14) for the ground terminal of that receptacle to your breaker panel is electrically sound, and even code compliant by the recent revisions of the NEC, IF and only if the case of your breaker panel is  bonded to an equipment grounding / safety ground system.
This is not a perfect test, but you could run an extension cord from that receptacle to your panel, and test for continuity / resistance between the neutral slot on the extension cord and the panel metal case.  You want to see continuity and very low (practically zero) resistance.