At the end of the day, you need to look at exactly what you want to do with the rest of your life, and be realistic. Is being a solicitor truly what you want to do? If so, all the very best with your LPC. I've got friends who I studied with who got 2:2s and are now practicing solicitors. They're not in the big international firms and they're not fabulously paid, but they weren't expecting to be given their grades and they enjoy their jobs. Other people from my course who didn't want to be solicitors are now legal executives and paralegals. On the other hand, I didn't enjoy the law part of my course at all and had no desire to go on and qualify. I'm now about to embark on a Masters in something completely different because that's the path that suits me. Please do really think about what you want to do before spending a load of money on the LPC. From what you've said in your other posts, maybe a job with a charity/in local government/in the Civil Service would suit you as it'd involve working with legislation and policy but you don't need an LPC. Law has so many transferrable skills that are really useful in jobs like this.
Re your mitigating circumstances, you probably should have gotten a medical certificate at the time, but this wouldn't necessarily be outlined on your transcript. If you visited your doctor and were treated for depression/stress-related illnesses, this would show on your medical record and a doctor might write a letter confirming when you were ill and you could tie this in with your study dates. It's a real long shot though. Also, if you did want to study for the Masters in IR, there are a few places that will accept you on a 2:2. For example, Keele and Oxford Brookes both accept those with a second class honours degree, whether a 2:1 or 2:2. They're not the best unis in the world (Keele is 43rd in the Guardian league table for politics, Brookes is 52nd) but they're not the worst either, and if you really want to do the course you may have to accept that your choices are quite limited but make the best of them.
Again, good luck in coming to a decision.