First, let me congratulate you for losing weight! It is not an easy thing to do and it's an even bigger challenge to stick with it and keep the weight off.
I think still feeling like you're fat, even when you're losing weight is a self-image thing and self-image is sometimes difficult to understand. It's easier to see things about other people sometimes than it is to see the same things in ourselves. Self-image is impacted sometimes by being in denial, or what is called "cognitive dissonance." This is your brain's way of protecting your psyche in the face of hurtful or disappointing circumstances. For example, most smokers know that smoking is bad for them. They know cognitively that if they continue to smoke, there will be unpleasant consequences, but they choose to smoke anyway. I am a recovering cigarette addict, so I know the things we say to ourselves when we choose to smoke in the face of overwhelming evidence that smoking causes heart disease, cancer and a whole host of other health problems: "I'll quit next week," or "I'm still young and in great health. I can smoke for awhile and I'll be okay." But until we get really truthful with ourselves, and admit we're essentially marching ourselves to a early grave, we continue to smoke.
Self-image also plays a very important role in how we feel about ourselves when we're overweight. I was obese for many years, and losing seventy pounds about three years ago has done wonders for my energy level and self-esteem. But you know, that fat guy is still there inside me. I still look in the mirror and think to myself, I'm still fat; even when my wife and friends (especially those who I haven't seen in a while) would tell me, "Hey you look great!" I am still cognitive of the fact that I've certainly lost weight, and I certainly feel better, wear smaller clothes and can walk up a flight of stairs without gasping for air. But I am in denial about it a little; I still think I'm overweight when I'm really not anymore.
Why? I'm not sure exactly. But I think that somewhere inside of me, I'm telling myself if I get too comfortable with the way I look, I might get complacent and start to put back on the pounds. And certainly, I know that when I don't watch what I eat and count the calories each day, or when I don't get my thirty minutes of high activity a day, I do start to pick up weight pretty quickly, and I just don't want to go there.
I don't know if this is how it is for you, but for me, I think I continue to be critical of my weight and size as a defense mechanism, and this keeps my edge so I won't ever become heavy again. Maybe that's part of the answer for you, too.
But for you (and me), we should take pride in our accomplishment! Losing weight is hard, and trust me, it gets harder with age. Be proud of yourself for accomplishing a great stride in your health and overall well being. Focus on the positive and keep at it. And I will too. I hope this helps a little.
I wish you well and bid you peace!