My Victoria plum tree is loaded with plums,

Victoria plums are prone to this in a good year and it's not good news. One of ours did the same several years ago and has never properly recovered.
I'd recommend you do what we didn't, and clean up the breaks and put some kind of wound treatment on to prevent canker or other fungal diseases.
In future, however hard it is to do, reduce the fruit after it has set so that the tree doesn't crop quite so heavily, or support the branches with props.