Yes, she is skinny and an unhealthy weight.
The four photos show a progressive loss of weight and condition. The second photo is not an unhealthy weight, but is pretty typical for a young horse in the middle of a growth spurt. The third and fourth photo are cause for concern.
I think you need to recalibrate your eye and gain a better understanding of weight and condition. A good place to start is by understanding body score. The University of Maine - Cooperative Extension Publications - Bulletin #1010, Body Condition Scoring for Your Horse
In the third photo, her entire backbone protrudes, and there are hollows both in front of and behind the wither. Compare that to the first photo, where the backbone is not at all visible, and there is flesh filling in the space behind the shoulder blade.
According to the body scale, the first photo is a 5 - 5.5, the second photo is a 4.5 - 5, the third photo is a 3 - 4, and the fourth photo is a 4.
The good news is that she is coming back from the condition in the third photo. The bad news that you're having trouble evaluating what you see accurately.
... might add that she was bone skinny when I first got her, so her growth has been stunted A LOT. Her sire and dam were nearly 16HH, and she is just a smidgen over 14HH.
First picture is after I had her for just a week, and she put on a good amount of weight.
Second picture was after I had her for two months. She started getting some fat and muscle.
If the first photo was after you had her for a week, she was not skinny when you got her, she was in good condition.
In the second photo, she has not *gained* fat and muscle, she has lost both fat and muscle, but it is within the range of normal if she also was having a growth spurt at the same time. If she did not have a growth spurt within that two month period, she just flat wasn't geting enough nutrition to maintain her weight, let alone grow.
In the third and fourth photos, there is absolutely nothing about her that "looks fat." There is nothing wrong with a growing youngster having a slight shadow of ribs, as in the second photo, but only if otherwise flesh and condition are good, which they are not in the third and fourth photo.
I would be having a serious conversation with an experienced horse person or vet and re-evaluate your feeding program.