I wonder if there is any phrase or sentence available out there to express that someone was always hiding or taking care my mistakes and silly things; to tell them that I am highly obliged.
— phrasal verb with cover US
to provide an excuse for someone, or an explanation for something that has gone wrong:
She would cover for her brothers when they came in late.
You've always been there to cover my back. That's really appreciated.
Using cover my back as a variant of cover your back which is someone protecting themselves from negative consequences:
cover your back BRITISH, AMERICAN or cover your ass AMERICAN, RUDE
If you do something in order to cover your back, you do it in order to protect yourself, for example against criticism or against accusations of doing something wrong. He had covered his back by persuading Evans, chairman of their finance committee, to provide a written approval for the contract. Newspaper editors have to cover their backs against accusations of libel.
Source: The Free Dictionary