Hungry AFTER eating!

Help!!! I am hungry all of the time, including AFTER I've eaten a full meal! Not even an hour after eating, my stomach is rumbling. I know the reason is because I don't eat enough fat or maybe even protein in my diet. (My diet is mostly lean poultry, shrimp, steamed vegetables, fruits, brown rice or buckwheat noodles, oatmeal) But even when I eat healthy fats like avocado or almonds, I am still hungry all of the time! I've tried drinking coffee to reduce my appetite but that doesn't work either. I drink tons of water and eat fruits and whole grains for fiber. My calorie intake is set at 1200 which I try to follow strictly. Maybe I'm eating too little (I'm 5'1")? I try to keep my meals under 350 calories. What are some healthy fats or protein rich foods I can add to my diet that won't bring my over my daily goal? Thank you!

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