As everybody can tell, you are emotionally stressed.
My first advice to you, calm down!. This is not the end of the world. You still have options.
You can go to industry if you want although I think you prefer not. You still have the passion for Academia since you are asking this question on this site. So, I am not going to suggest that.
If you want to stay in Academia, others have given you excellent answers. I am not going to repeat them. I want to point out things others may have missed.
First, you have to admit that you messed it up. How to re-enter Academia is your question. I think you'll have to look for the schools in the next lower tier. Transferring to a school of the same tier may not be possible at this time. For example, if you are in the top 20, apply to the top 50. I think you have the chance. If you still don't get to top 50, go to top 100. There is a will, there is a way!
Go to your advisor and tell him you would like to transfer to another school. Tell him that you made a mistake and want to restart your academic career somewhere else. He will be glad to help you to transfer because he has some responsibility to fulfill. At least, you were his student.
Again, calm down. Being emotional will not help you. Find another school is your first priority. Good luck!
Let me address your specific issues here,
And what to tell about my messed up situation in applications? Is it recommended to apply to other schools without mentioning that I had attended this one?
Your question boils down to, Can I erase my past?
My answer is no. You can't. The key is the recommendation letters. Whom do you go to for those letters? The people who knew you during your undergraduate days? They know you were in your current school. Are they going to wonder what happened to you in the past couple of years? In these days, information travels fast. A couple of e-mails between your undergrad prof. and the profs. in your current school will reveal everything. Get help from your current school to transfer to another school is the practical solution.
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