Is it correct to say "I feel painful" to mean "I feel pain"?

Is it correct to say "I feel painful" to mean "I feel pain"?

Please note that I mean only those cases, in which the phrase is a complete sentence. There should be no words after the last word in each quote (like in "I feel painful pulses in my head", "I feel painful burning sensations in my stomach", etc.)

If it's correct, what is the slight difference in meaning there?

No, it is not correct English to say "I feel painful."

You can say "I feel pain", or "I am in pain", because 'pain' is a noun, but "painful" is an adjective so you would need to use it qualify something else (as in your "I feel painful sensations" example).

If you feel pain you hurt. When, say, getting over a case of the flu one might say "I hurt all over." If you sprain your ankle you'd say "my ankle hurts".