You may also need to double check the feed amount as over feeding of a higher meat content food will cause loose output and often reducing by only 10% can settle things down.
I agree with that.
The fact that your pup's digestion improved on a hypoallergenic diet does not, in my opinion, prove that her problems were caused by allergy or sensitivity, only that they might have been. There are two other possibilities...
First, as suggested above, your pup's symptoms could suggest that she was just being overfed. Too much food does not always cause weight gain, esp in puppies, often it just results in loose stools or even diarrhoea. I have used Applaws in the past, though only for a short time, and I found their feeding guidelines to be hugely too much for my own dogs, so that does sound quite likely to me.
Second (and I know David Green will disagree with me here
), I do think that a small but significant minority of dogs simply cannot tolerate dry foods with a very high meat content like Applaws, Orijen, Eden etc., they find them too rich. If this applies to your pup you might find she gets on far better with a slightly lower meat, grain free food like Acana Regionals or one with a small amount of eg brown rice such as Gentle.
I have myself experienced this in the past with one of my standard poodles, the vet said hypoallergenic only after a trial on a vet diet, but she turned out not to be sensitive to anything at all, it was simply that the food she had been getting was too rich for her - I refused to accept the vet's opinion and switched her to Acana, and she did far better on that than the vet diet.
Whatever you decide to try her on though, do it cautiously. Try to get a sample, or at least a very small bag, and just mix a tiny amount in with the hypoallergenic food at first, and see how it goes.