If it's a survival situation, by all means , eat the lips, brain and flesh from the skull, or de-scaled the skin is the best part of it Assuming a Europeon carp, that is. And the eyes.
What one does not throw up, may be valuable nutrition.
I was a self taught fisher in my teenage years in the Cumberland River in Kentucky. During this time of year, late summer, I learned that I could catch a carp on nearly every cast by using corn for bait, right before dusk.
In Kentucky I was eventually told that white people do not eat carp, only black people do. I also was told that they are supposed to be skinned before eating, and that the streak along the side of the fish can be poisonous.