I found this statement interesting. Can you define what real hunger is for you? What I mean is what are you actually feeling?
I'm not claiming to be an expert, but I sometimes think we overuse this concept of "head hunger" vs. "real hunger". I know I've been guilty of that as much as anyone, but i think we should keep in mind that much of what people call real hunger is also "in our heads".
A better way of differentiating hunger signals may be to call them homeostatic hunger and hedonic hunger since these happen somewhat differently.
While this is oversimplified, homeostatic hunger starts as a signal from our stomach by way of production of ghrelin, which in turn activates AgRP neurons in the hypothalamus. Simply put, it may originate when the stomach is empty, but it's our brains that tell us it's time to eat again. This is not something we actively control. It's the bodies way of trying to keep you from starving to death.
Hedonic hunger on the other hand is your body seeking pleasure from food. We like to say this is the one we want to control if weight loss is the goal, under the assumption that overall calorie intake will be less if we don't "give in" to cravings. Here's the thing, though. While scientists don't fully understand what's happening, we do know that dopamine and endocannabinoid receptors are being activated in our brains. Interestingly, just seeing or smelling certain foods can trigger these same processes.
I wanted to explain this because it wouldn't be wrong to say all hunger is head hunger. The good news there is we also can be in control of both types of hunger, since they are both "in our heads".
In terms of your specific situation, I think it would be rare to already be experiencing a lot of homeostatic hunger this early after surgery. On the other hand, it's probably not unheard of.
For me personally, I was really bad at understanding what true hunger felt like. As a former obese person, I hated feeling hungry and would rather feel the overstuffed feeling in my guts since at least then my brain would quiet down. I'm not saying I've got it mastered, but I'm beginning to understand that when I'm truly hungry, I have other things going on like feeling weak, feeling irritated, and/or having brain fog. The strong urge to eat that i sometimes feel without those symptoms is probably more just my brain trying hard to either seek pleasure, or keep me from starving to death.