You can get in somewhere, somehow. Do you have geographical restrictions?
I don't know that 3rd tier is realistic, but there's probably a school somewhere in the 4th tier that will take you.
I could even envision a scenario where your previous grades are acknowledged, but not transferred to your new school's transcript since most schools don't include other schools' grades on their class rankings, etc.
Just keep applying. You may have to move to a new part of the country, though. Use your personal statement to explain what happened. You're not the first person to have a difficult time due to health issues of a relative. In a somewhat related way, I left school one semester when I found out a relative, who had raised me, had only a couple of weeks left to live. I asked all my profs if they would give me their final exams early. They were all very kind and obliged, but since I took the exam with 3 weeks to go, I got straight Cs that semester.
You're not the only one this happened to, and the admissions committee has seen it before.
Fortunately for you, 4T schools need to put butts in the seats. If your UGPA and LSAT are good (and I presume they are if you were previously admitted to a 2T), then you can probably find a school that will take you.