Carrying some sort of trauma kit is a good idea. I would definitely recommend getting training and carry some basic medical items.
Here is a very good video done by the late Paul Gomez on his very minimal yet effective daily carry trauma kit.
I live in a state that does not allow me to carry on my person and I still carry a similar trauma kit.
"All the great things are simple, and many can be expressed in a single word: freedom, justice, honor, duty, mercy, hope." -Winston Churchill