“feel tired” vs. “am tired”
Solution 1:
Let me put it this way:
He is feeling dead. Means he is not dead, but is feeling like it.
He is dead. Means he is dead. Period.
Feeling tired means you are feeling like tired or tiredness is slowing taking over you. In the other example you are tired and don't want to give further explanation. There's nothing more to it:)