I don't see info about how long you have been sleeved.
I'm 4 months out and I can honestly say I experience hunger much more now than I ever did before I was sleeved... and I mean in comparison to pre-sleeve dieting. I think the thing that concerns me about your information is that you experience the hunger all the time. I don't. First, I also absolutely know mine is not head hunger because I'd eat anything if I could. When that hunger is gnawing at me, green Beans would be wonderful. In fact, I don't really crave any "before surgery good food". The only single item I miss is diet cola. And I'm pretty sure my frequent hunger is due to my small capacity.
One hour ago I had 1/4 cup egg substitute and 4 trisket crackers. That totally filled me up. Now, I should not eat for 2 more hours. I can promise you that in one hour I will be hungry. And I'm pretty sure it's because I need more than 500 - 600 calories a day. To make this even less fun, I'm not losing much weight and never have. I think that after my initial 6 weeks on liquid my body just rolled into starvation mode (2 weeks pre-surgery, 4 weeks after). I think I'm being given the hunger signal to try and make me fix the problem. Basically, I think my body is not stupid enough to think 560 calories a day (yesterday's count) is enough long term in spite of me trying to make it think it is!
But the key is that after I eat, the hunger is sedated for at least an hour, sometimes two. I'm never hungry while I'm eating.
I don't doubt you are experiencing real hunger. But I have no clue what the issue is and it's great that you are checking in with your doctor. I guess I'm just posting my experience so that others who are pre-sleeve know that this might not be the cure for hunger if that's their motivation in having the surgery. I am surprised by how much and how often I am hungry but that was not my main issue. I did this for the portion control part and man, I got that in spades!