I think you are looking for the word strain. At the moment, I am unable to find a definition that explicitly includes "holding your breath", but at the very least I believe it is implied. It is also included as a symptom of constipation on WebMD.
One would also strain while trying to lift heavy objects.
I find definitions like this
1 [with object] Force (a part of one’s body or oneself) to make a strenuous or unusually great effort:
It is not explicit about the "holding your breath".
I found another case where it is used with boxes:
If you have to strain to carry the load, it's too heavy. [1.].
Here are a few images I got from googling "straining":