I am 44 years old and am on anxiety medicine but otherwise very healthy. This last week I started having difficulty getting a deep breath. I have a physical job but even when I am doing nothing it still seems to happen. Just wondering what it could be?

Based solely on what you have posted (and not personally having medical expertise), it may be possible that the shallow breathing could be a side effect of the anxiety medication. But only a physician can make that determination or find another cause.
This link briefly describes a relationship between tranqullizers and breathing symptoms.
Prescription Sedatives Tranquilizers | The Partnership (http://www.drugfree.org/drug-guide/prescription-sedatives-tranquilizers)