Good to hear from you. 

Here is the last sentence:

In addition, I provided the necessary paperwork via a computer and checked vital signs, drew blood, and gave shots.

What you have here is a list. In it, you have four verbs “provided,â€ “checked,â€ “drewâ€ and “gave.â€  

You could delete the “andâ€ to make a list of four activities: I provided the necessary paperwork via a computer, checked vital signs, drew blood, and gave shots. 

However, I saw it as two somewhat separate activities (paperwork as an administrative task and then three medical patient-related tasks).

Sort of like this: First, I provided the necessary paperwork via a computer, and then I checked…etc.

Perhaps I should have added “thenâ€ to the original edit because you are talking about a process that starts with the paperwork and is then followed by the medical procedures.