Both sentences are correct, but they convey slightly different meanings:
"I am feeling blue."
This expression means that you are feeling sad or down. It's a common way to express that you're experiencing sadness or a low mood.
"I am blue."
This sentence can also be used to convey that you're feeling sad or down, but it's a more direct and simple way of saying it. It might not be as common as the first expression, but it's still valid.
So, it depends on the level of directness and simplicity you want in your statement. If you want to be more explicit about your emotions, you can say "I am blue." If you want to use a more idiomatic expression, "I am feeling blue" is a good choice.