I had a similar problem with my second to last job. It was a tech support job. Our company made our own systems inhouse and then shipped them to clients. Clients typically were car dealerships, so the big issue for me was that if someone called and their shit wasn't working, I'd get yelled at for a while because I was costing them sales.
(Coincidentally, my favorite story was a guy calling me on December 26 - yes, December-f*cking-26 - about how his stuff wasn't working, I was costing him $10K/hour, until he finally screamed out "YOU DON'T UNDERSTAND! IT'S TOYOTATHON!!!!!" at which point I put him on mute and laughed my ass off).
Back to the situation at hand...
I worked Saturday shifts, which essentially meant I was there when no one else was. I usually liked these because it was quiet, I'd sleep half the time and let the machine get the calls, then use the rest of the time to eat lunch, play Gameboy, take a shower (yes), and then finally call people back with assistance. It sounds worse than it really is.
Anyway, a guy calls me, tells me he has a problem. I was kind of new and hadn't heard of this issue, so I told him I'd call him back. I call about 2 other techs at home, get some information, call him back, solve the problem. Absolutely no further issues.
Well, a few days later I guess his hard drive melted or something, because he calls back and says he has another issue. A different tech answers (I was at school that day until my shift, which started at 3PM) and basically tells the guy he's SOL and has to get it sent in, probably giving him about 4-5 days of downtime. The customer ERUPTS in anger, screaming at the guy, demanding to know why he has to put up with this kind of poor service, etc etc etc. To top it off, he screams about how "the tech last Saturday didn't know shit and told me to f*ck off." He then faxes in a 3 page rant talking about how I didn't help him at all, how I told him a number of things I didn't say, how we suck as a company, how he's been a valued customer forever, bla bla bla, etc etc etc.
So I come in at 3PM and my manager says he has to talk to me. He explains the situation to me. I tell him my side of the story and made it clear I did nothing wrong. Regardless, he tells me I have to sign a sheet saying I understand and agree to what I did wrong, that the situation was my fault, and that we had probably lost a customer on my behalf. In addition to all of this nonsense, he told me I could no longer work Saturday shifts, which constituted 7 hours of my 20 hour minimum required hours per week quota.
I told him there's no way I can make the hours up M-F because school comes first. This was the truth - I had a terrible schedule that semester, the only way it would have worked would have been to come in at 6AM-10AM on 2 different days, something I wasn't going to do since work was 30+ minutes from my house and I typically didn't get home until 7-8 at night after classes anyway.
He just shrugged and said "well we can't have you on Saturdays anymore so you need to make it up" and walked out of the room.
Long story short, turned in my two weeks notice the next day, but they let me go the day after (a Friday), something that I didn't mind because the pay wasn't worth two more weeks of that kind of irritation.
Upon speaking with others and my parents, I learned that as an employee, I don't have to agree to shit, and I should have refused to sign the waiver. Good knowledge to know for the future.
To OP, sorry about the circumstances, we've all been there and it sucks. Unless you really think burning bridges is a good idea (and it may well be), the best thing you could do would be to talk to some sort of mediator privately. I don't know if your company allows such things but a number of them should these days, or at least a way to anonymously recommend something off the record.
