how much do you actually weigh? because 20lbs in a monthish is a lot of weight to lose. i'm going to call it 5 weeks, which means you're looking at a nearly 4lb loss per week. which is reasonable to expect if you weigh over 400lbs. but if you're closer to 200lbs, that's about twice as much as you can expect to be reasonably able to lose. while it's possible to do for a bit, immense hunger in this sort of scenario is your body's way of telling you to feed it more. and the answer in that scenario [you weigh right around 200lbs or less] is that you should be eating at least 500 cals more per day.
if you do have a lot more weight to lose, the fact is that foods don't fill everyone up equally. in other words, some foods will keep you fuller longer than others, and what works for one person doesn't work for everyone. so what you should start doing is keeping a food journal [or adding to the one you already use]. include not only the foods and amounts, but also the time you eat. make another note when you start to get hungry again. get some data and then start to look at what is keeping you full the longest and what is leaving your the quickest. then start to work to tweak the meals that are underperforming or even eliminating them in favor of foods that do keep you full.
you may also want to start looking at a hunger satiety scale and keeping track of where you are. because sometimes, it can be easy to associate "not stuffed to the gills" as "hungry," when in fact there is a lot of play between hungry and stuffed.
if you're a woman, it's also possible that this could be in some way connected to your fertility cycle.
and i'm not sure where you came up with 1500-1600 cals, but it's possible that might not be enough for you. if you're a fairly small and inactive woman with little to lose, it might be just right. but if you're taller or younger or pretty active then it may be too few calories. again, without knowing your sex, height, age and weight it's hard to say. depending on all that 1500 can be too many or too few.
-google first. ask questions later.