Doctors and nurses won't feel less of you because you fainted and hurt your arm. I have fainted too. I was feeling overly stressed and blacked out. I told my doctor about it and she told me that she has a number of patients have fainted due to anxiety.

Don't feel ashamed that you are stressed. Anxiety is part of us. We didn't choose it. It is like having vision or hearing problems. Doctors and nurses see patients that have anxiety all the time and they see hundreds of patients. Most of them will treat you kindly.