It should be "I've got everything covered (here)." I've is grammatically correct, but many people, amongst close friends, will say "I" instead. "Here" is fine, but not necessary unless the person really wants to indicate they are discussing things at a particular place. The idiom "got XXXXXX covered" means that you have whatever XXXXXX is (in this case everything) under control. It is used to indicate that you do not need assistance in a matter, you are okay handling it by yourself. "The line really seems long, will you be able to handle the customers without me??" "Don't worry, I've got the customers covered."

would you please tell the whole context?

I think it's another way of saying I have everything under control here. :)