I do not want to burst your bubbles. Where do you live?
Have you read this thread.
Apricot tree death in the northeast
In some areas, like the Northeast, keeping apricot trees alive can be challenging.
Once they survive, their blooms may get wiped out by late frost as apricots tend to bloom too early for its own good.
I don’t think that’s a rabbit damage. For stone fruit, oozing gummy substance can be anythings from too much water/rain, physical injury to the tree, to canker issue, etc.
If it is canker, make sure you keep your tree healthy so it could fight off the disease and recover.