All of the advice above is great -- everyone is different, so one of those ideas may work for you.
I was diagnosed just under 5 years ago, on insulin for the last 4.5 years. Since diagnosis (even before I started insulin), I, too, always feel hungry. I can even feel hungry after a very large meal - so 'full' and 'hungry' at the same time. I have not yet been able to determine the cause. My thyroid function has been tested multiple times, and it is fine. I have modified my diet to be more low-carb, higher fat, without any noticeable improvement in this area (though my total daily dose (TDD) of insulin has gone down by 45%).
I did speak with my endo about trying Symlin; however, in his experience with other patients, he did not see noticeable improvements. He, therefore, did not encourage me to try it. I have not been tested for Amylin level, though I believe such a test is available, if rarely ordered.
For my part, I have stopped using hunger as an indication as to when and how much to eat. Sure, there are times when I am "extremely" hungry, and that is somewhat meaningful (usually indicative of low or rapidly going low BG...), but the rest of the time, there is a near-constant lingering "hungry" feeling that just won't quit. I drink a lot of water - sometimes that satisfies temporarily, sometimes not. I snack on nuts, though not frequently, since that, too, hasn't helped me. I generally select foods and quantities based on what I think I should be eating, rather than what I "need" to eat -- that, at least, stopped the weight gain and helped turn it around a bit. I schedule my meals, rather than eat to my hunger. Not always successful, but close, most of the time.
I am changing endos, as my old doctor is retiring. This is definitely going to be on the agenda for the new doctor.