It is probable that your bird has been undetectably sick for some time, because in the wild, a bird would hide their illness because they are a 'prey' species. If they didn't do this, they would be picked as the next target by the predator. Even our hand-raised babies still harbor this instinct, so when your bird started 'puffing up' etc., that was her way of showing how sick she was; when they reach the point where they don't care about hiding it they are really quite ill.
If your new budgie has spent most of her young life eating a predominantly all-seed diet, they very well may already be showing signs of nutritional deficiencies, manifested by breathing and neurologic problems. You may be
seeing signs of Hypovitamosis A and Hypocalcemia (not enough A or Calcium in the diet). She may have an enlarged liver which is overburdened with fat (hepatic lipidosis). And on top of all that, we do not know if she came with any infectious diseases, or genetic defects (like a heart problem). There may have been an unseen trauma, or your bird may be suffering from heavy metal poisoning.
Whatever the cause you need to see a vet (www.aav.org/vet-lookup) ASAP.
In the interim, increase the room temp to 80F/27C, and place all her favorite foods and water well within reach. It is important to change the water frequently as it may become unappetizing if it gets really warm. Place a soft towel on the cage floor and lower the perches, or move to a makeshift hospital cage (plastic bin, padding, no perches etc.).
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I am so very sorry for your loss These little creatures leave such big holes in our hearts when they are gone.