So I was playing my guitar through my amp, at a quiet volume when suddenly, in mid-playing, my amp began to buzz. You know when your amp is on, and you touch the cable directly before connecting to the guitar and it makes a buzz. Yeah, it was that kind of buzz. I used some different cables and the same thing happened. Then I tested with a different guitar and no buzz.

And the weird part is that if I hold the guitar in a different position, sometimes the buzz goes away. And if I tinker and wiggle the cable inside the guitar jack, sometimes it also goes away. I'm not sure what to do and it's not my own guitar so I wanna try and fix it. If I take it to professional, I'll have to tell the person I borrowed it from first which will be embarrassing as I assured him I can take care of it. And it's not my fault because it started suddenly and I didn't hit the guitar or move or anything.
Sounds like something with the input jack. Its not something that necessarily occurs from mistreatment, its fairly common so you dont need to be embarrassed about it.

Just take it to a tech, it'll be a quick and inexpensive fix.

Or maybe techy types on here will be able to advise you how to fix the problem yourself? Might just need a clean
Oh I also noticed something else. After I connect the cable the buzzing starts. HOWEVER, you know the side of the guitar output jack, the metallic part with the screwdrivers? Well if I touch that with my fingers, with my feet on the ground, the buzzing goes away.
the metallic part with the screwdrivers? Well if I touch that with my fingers, with my feet on the ground, the buzzing goes away.

It seems that your wiring system is not grounded. Is that a new guitar? Check the back of the guitar and try to look if the ground is missing.
No it's not a new guitar. It's actually more than 5 years old and it was working perfectly before today.
Sounds like a grounding issue. Or the control cavity isn't shielded. Open up the control cavity and tell me if there's tin foil looking stuff on the inside of the cavity.
Gibson RD Silverburst w/ Lace Dissonant Aggressors (SOLD)
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Yeah there is tin foil on the cover. The weirdest part about this is that it happened out of the blue. I was playing it perfectly for 1 hour and suddenly, in the middle of a song, it just happened. I didn't suddenly knock it or anything.
The kinds of things that cause this are 99% of the time things that you can't fix without some knowledge and tools. It's good to know how to fix things yourself, but it is time consuming and involves a learning curve. My guess would be a faulty jack or loose wire. But to fix or replace that, you have to not only find it, but also fix it. You will probably need at least a soldering iron. You will have to learn to solder, especially since it's not your guitar and I presume you want a reliable fix. For now, for these reasons, and out of respect for the owner, I recommend telling the owner and letting them decide. It's not your fault! But if it mysteriously fails later on because of something that you or the tech did, it's really unfair to the owner.