It sounds as if you suddenly realized the level of rigor needed to get into tippy-top schools, and tried to make up for a previously middle-of-the-road high school record by taking an extra-heavy courseload senior year. (Six academic classes, three of which are AP’s.) It got to be a bit much (and a relative being ill may have been a factor, though you did fine in the other five classes and TBH you make it sound like this is just an excuse that’s available rather than something truly traumatic - though perhaps you’re just being reticent in this forum about something genuinely upsetting)… and you made a big error of judgment, tried to cut corners by cheating in what you probably saw as a lower-priority class, and got nailed.
The thing is that even before this incident, the late-bloomer path was not going to get you into most of the schools you applied to, unless you have another really significant “hook” that you haven’t disclosed here. There are many great schools that you could qualify for this way, but if you have shifted into “Ivy or bust” mode late in your high school career, you might want to consider applying for a post-grad year at a competitive prep school. Such a school would offer plenty of advanced courses beyond the ones you are taking now, both to prove your academic mettle and to gain more depth in your areas of interest that you hope to pursue in college. This would give you another year to regroup and mature, as well as access to a crack team of guidance counselors whose whole goal in life is to get kids into those uber-competitive schools. If you are young for your grade, that would be another point in favor of a regrouping year, if it’s something you can afford financially.
On the other hand, there are plenty of great colleges out there that you could get into with your current record - you just didn’t focus your applications in that direction. You will most likely get into Riverside, or at least get a backup offer from Merced if you qualify for the ELC guarantee, which you probably do. There is absolutely nothing wrong with going to either of these UC’s! For that matter, there would be nothing wrong with going to a community college and taking the guaranteed transfer path into one of the more competitive UC’s. You can get a terrific education through either of these paths. (Just don’t start out at Riverside or Merced in hopes of transferring to a different UC - that’s very difficult to do.)
If you can re-calibrate your expectations and be okay with the above, then there’s nothing you really need to do now but wait. I agree with others who have recommended against the “sick relative letter.” The big public U’s won’t even read it, and the privates won’t buy it.
If you can’t make your peace with the Riverside/Merced/CC path, then you need to lurch into action and look for some moderately-competitive schools you like, that you can still apply to. There are so many that I wouldn’t venture recommendations without knowing more about what you want to study, standardized test scores, financial constraints, and so on.
You will be okay, particularly if you take this life lesson to heart. It’s not the biggest setback in the world, and who knows, maybe it’s saving you from a much more costly mistake in the future.