Well... of course, as soon as I post this I find a list from the Arbor Day order (or at least, I think it was that year's order). No idea which is which (which of the ones that came in this bundle actually survived), but could the third photo be a young Sargeant Crabapple? That's on the list, as is Eastern Redbud, Washington Hawthorn, dogwood (I know it's not that), Goldenraintree and crapemyrtle (I remember wondering why on earth they were shipping crapemyrtles to New England!!) In theory (meaning assuming they sent what they said they were sending), it should be one of those -- and the crabapple seems like the only one it could be? I'd be floored if they were shipping free Bradford pears (which is what someone on Name that Plant thought it was as well) -- aren't they considered more or less invasive plants in a lot of areas these days? So I'm hoping for Sargeant crabapple since I wouldn't mind having one of those for the birds (means the little guy can stay right where he is now, in the bird/butterfly garden).

Click here this thread should answer the question.

Mimosa wilt has been reported in California, notably southern CA, though the lack of characteristic symptoms noted in the OP makes this less likely. I'd avoid any cultural changes that might accelerate the tree's decline. As for planting A. julibrissin anywhere where significant disease problems have been reported, it would be best not to give the tree a prominent location, and to accept that it might have a limited life span (someone living about a half mile away from us had a huge old tree in their front yard that went from magnificent to dead over the span of three years). I have two specimens of "Ernest Wilson" grown from seed started three years ago, planted in two out-of-the-way locations. Both survived -9F this past winter with virtually no damage. There are cultivars i.e. "Flame" and "Union: which are said to be wilt-resistant. As for invasiveness, in my part of Kentucky I don't see self-seeded trees growing along roadsides and in "waste places" as described further south.

Generally speaking, without closeup picture of the leaves, buds, bark and flowers, we can still most likely presume this is some kind of plum or cherry trees. These belong to the Rosaceae family of which there are 4,828 species in 91 genera, including apples. So, if those trees are the source of the problem, you'll have quite a time protecting him/her from this type of allergen because these are ubiquitous. (There is a 'Name that Plant Forum' on these boards). Have you seen the pup eating or chewing on plant materiel or anything else that might upset his stomach? Many kinds of plants can have a mildly to modest toxicity if taken internally and if they eat grass, they can vomit from that. It might be best to keep the pup out of the yard during pollination time, but sorry, I am not a veterinarian and have no idea if pollens from these trees can cause any of the symptoms you describe.