No, you can't, it makes no sense in most situations. It is like in English you say "Me good". And you have no guarantee to be understood, even if you don't care about being correct grammatically.
In Russian impersonal sentences are used much more often than in English.
Literally it looks like:
"У меня всё хорошо" = "With me everything (is) well" = I am fine.
"У меня машина" = "With me (there is) a car" = I have a car.
(Or maybe "by me...")
That is the most natural way to say (and to think about) in Russian.