Hi and welcome to the forums.
First, don't capitalize "hungry." That alone makes it incorrect.
I can be correct in the right context.
Imagine two people are travelling in a car. The driver asks if his passenger is hungry, and whether it's time to stop for dinner. The passenger does not want to create a fuss. He says, "Well, I'm a bit hungry, but whatever is convenient for you."
The driver says, "I'm hungry myself, so let's stop at the next place that looks good."
The "myself" adds emphasis. He could have said "I too am hungry."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.